V.D. Blondel and J.N. Tsitsiklis, A survey of computational complexity results in systems and control, Automatica, 36, 9 (2000), 1249--1274.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....UMDP. The two actions a and b have identical dynamics, denoted by the matrix M below, but their reward vectors R a and R a are di erent: M = 6 6 6 6 3 0 3 5 9 1 3 1 9 1 4 1 4 1 7 7 7 7 ; R a = 7 ; R b = 1 1 0] 2. 4) The unique stationary point of the matrix is at [ 2 3 22 4 11 ] (i.e. 2 3 22 4 11 ]M = 2 3 22 4 11 ] and the matrix is ergodic, that is, all points of the simplex converge to the stationary point with repeated applications of the matrix: 8x 2 X ; lim i 1 xM = 2 3 22 4 11 ] Due to identical dynamics, the action that yields the ....

....a and b have identical dynamics, denoted by the matrix M below, but their reward vectors R a and R a are di erent: M = 6 6 6 6 3 0 3 5 9 1 3 1 9 1 4 1 4 1 7 7 7 7 ; R a = 7 ; R b = 1 1 0] 2. 4) The unique stationary point of the matrix is at [ 2 3 22 4 11 ] i.e. [ 2 3 22 4 11 ]M = 2 3 22 4 11 ] and the matrix is ergodic, that is, all points of the simplex converge to the stationary point with repeated applications of the matrix: 8x 2 X ; lim i 1 xM = 2 3 22 4 11 ] Due to identical dynamics, the action that yields the higher reward is the best ....

[Article contains additional citation context not shown here]

V. D. Blondel and J. N. Tsitsiklis. A survey of computational complexity results in systems and control. To appear in Automatica, 2000.

.... nite automata have found applications in several di erent contexts, including the study of the power of randomizing in algorithms, space bounded proofs and Arthur and Merlin games, rational series and semigroups of matrices, as well as Markov decision processes and probabilistic planning [19,25,15,8]. 31 It is now well established that optimal planning without full observability is prohibitively dicult both in theory and practice [40,29,32] These results suggest that it may be more promising to explore alternative problem formulations, including restrictions on the system dynamics and the ....

V. D. Blondel and J. N. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36(9):1249-1274, 2000.

....natural problems, in mathematics and computer science were found to be undecidable. Some of the undecidability results in control theory were obtained by reduction from a counter machine, see Blondel et al. 6] For a survey of decidability results in control theory area see Blondel and Tsitsiklis [7]. A counter machine is described by 2 counters R 1 , R 2 and a finite collection of states S. Each counter contains some nonnegative integer in its register. Depending on the current state s S and depending on whether the content of the registers is positive or zero, the counter machine is ....

V. D. Blondel and J. N. Tsitsiklis, A survey of computational complexity results in systems and control, Automatica 36 (2000), no. 9, 1249--1274. 20

....modeling when it is formulated for a single agent, it reduces to a regular POMDP. The latter have been thoroughly studied under numerous limitations of the model s parameters. The research has produced a wide range of complexity results for control problems of POMDPs, from polynomial bounds [5, 9, 17] through undecidability bounds [14] Other distributed models, similar to Dec MDPs, have been considered as well. For example, Littman [11, 12] describes multi agent systems as Markov Games [22, 15, 21] and by applying variations of the Qlearning algorithm[23, 24] an optimal policy in a game ....

....Madani et al. prove that finding an exact policy of any sort for infinite horizon POMDPs is undecidable, and the result naturally carries over to any extension, e.g. Dec POMDP with infinite horizon. On the other hand, approximate solutions to POMDPs with infinite horizon are indeed tractable [5, 9]. Therefore, considering a process with an infinite horizon, it remains an open question whether approximating decentralized control is tractable as well. Moreover, the implementation of MIPs as models for multiagent systems can guide us in other computational complexity related topics not yet ....

Vincent D. Blondel and John N. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36(9):1249--1274, September 2000.

....designing robust controllers for uncertain systems. 1 Introduction It has recently become clear that many control problems are too difficult to admit analytic solutions [2] New results have also emerged to show that the computational complexity of some solved control problems is prohibitive [3]. Many of these linear and nonlinear control problems can be reduced to decidability problems or to optimization questions, both of which can then be reduced to the question of finding a real vector satisfying a set of polynomial inequalities [20] Even though such questions may be too difficult ....

V. Blondel and J. Tsitsiklis. A survey of computational complexity results in systems and control. to appear in Automatica, September 2000. 11

....feasibility or optimality problems, provided that the rank constraint is dropped. These constraints are nonconvex and can greatly increase the complexity of solving our optimization problems. For instance, several well known NP hard problems can be formulated using rank constraints. We refer to [7, 72] for complexity results in systems and control. Alternating projection algorithms can be used to enforce these hard constraints on the solution [26] Note that these algorithms can only guarantee a local convergence to a feasible solution, which might be suboptimal. In general, optimization ....

Vincent D. Blondel and John N. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36(9):1249-1274, 2000.

....Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technick a 2, 166 27 Praha 6, Czech Republic. This work was supported by the Barrande project No. 2001 031 1 and by the Ministry of Education of the Czech Republic under project No. LN00B096. 1 constraints [Blondel and Tsitsiklis, 2000]. Similarly, the problem of SS by output feedback was shown to be NP hard, the most negative result in this direction being that the SS problem for more than two plants is rationally undecidable [Blondel and Tsitsiklis, 2000] A lot of work has been devoted to SOF design and SS, but we are not ....

....of the Czech Republic under project No. LN00B096. 1 constraints [Blondel and Tsitsiklis, 2000] Similarly, the problem of SS by output feedback was shown to be NP hard, the most negative result in this direction being that the SS problem for more than two plants is rationally undecidable [Blondel and Tsitsiklis, 2000]. A lot of work has been devoted to SOF design and SS, but we are not aware of any result on the combined SOF SS problem. The purpose of this note is to show that, in the special case of single input single output plants, both SOF design (traditionally approached with graphical root locus ....

V. D. Blondel and J. N. Tsitsiklis "A Survey of Computational Complexity Results in Systems and Control", Automatica, Vol. 36, pp. 1249-- 1274, 2000.

....shown very early (see [7] 18] that linear programming could be used to solve problems involving MDP s with finite state and action spaces, in particular for the ergodic (average cost) case. As recalled by Blondel and Tsitsiklis in a recent survey of computational complexity results in control [5] . linear programming is the only method known to solve average cost MDPs in polynomial time. However the linear programs (LPs) associated with MDPs are quite large and may su#er from ill conditioning when the Markov chains contain strong and weak interactions, that is transitions probabilities ....

Blondel V.D. and J.N. Tsitsiklis, A survey of computational complexity results in systems and control, Automatica, Vol. 36, No. 9, pp. 1249-1274, 2000.

....estimator performance. A major challenge is to determine whether this can be done in a computationally efficient manner. From recent work in the control field, it appears that determining filters which provide optimal robustness to highly structured uncertainties can be computationally expensive [1]. An alternative to the Kalman and H 1 filtering methods is to find a robust Kalman filter which 1 minimizes (an upper bound on) the variance of the estimation error in the presence of a system model with norm bounded structured parametric uncertainty and norm bounded uncertainty in the ....

....both formulations led to filters with similar behaviour and performance. 4 Numerical Examples In this section, the performance of the proposed robust state estimation method is illustrated via simulation results. Two numerical examples are given here, the first one is the same example used in [1] and [2] the second one is a target tracking example. 4.1 Example 1 In this example the following discrete time linear uncertain state space model is used x i 1 = 0 Gamma0:5 1 1 ffi # x i Gamma6 1 # u i ; jffij 0:3; y i = Gamma100 10 ] x i v i ; 4.1) s i = 1 0 ] x i ....

[Article contains additional citation context not shown here]

V. D. Blondel and J. N. Tstitsiklis, "A Survey of Computational Complexity Results in Systems and Control", To appear in Automatica. Also available on the World Wide Web: http://web. mit.edu/jnt/www/complex.html.

....####### ######### ############ ####### I. Introduction It has recently become clear that many control problems are too dicult to admit analytic solutions [12] 15] 17] 56] New results have also emerged to show that the computational complexity of some solved control problems is prohibitive [16], 24] 61] Many of these (linear and nonlinear) control problems can be reduced to decidability problems or to optimization questions [10] both of which can then be reduced to the question of nding a real vector satisfying a set of (polynomial) inequalities. Even though such questions may be ....

....be demonstrated that a candidate solution can be veri ed in polynomial time. In control theory, researchers have followed this reduction method to study the computational diculty of some decidable problems and many decidable control problems have been shown to be ## complete (or ## hard) [16], 24] 49] 51] 61] A recentoverview of the computational complexity of many control problems may be found in [16] The problem of simultaneous stabilization of # given linear systems with a LTI dynamic compensator is as previously mentioned rationally undecidable for # # 2 [12] However, ....

[Article contains additional citation context not shown here]

V. Blondel and J. Tsitsiklis. A survey of computational complexity results in systems and control. Preprint available at http://www.ulg.ac.be/mathsys/blondel/publications.html, 1998.

....system. The emphasis is put onto practical implementation issues and numerical properties. 1 Introduction It is now widely recognized that most of the problems in robust control cannot be solved in a reasonable amount of time when problem dimensions are reasonably large, see the recent survey [2]. Several approaches have been pursued to get through this fundamental bottleneck. Some researchers decided to rely on probabilities and statistics, some others are further improving global optimization strategies to cope with larger problems at a lower computational cost, some others are rather ....

V. D. Blondel and J. N. Tsitsiklis "A Survey of Computational Complexity Results in Systems and Control", Automatica, Vol. 36, No. 9, pp. 1249--1274, 2000.

.... is probably the most general representation of the parametric uncertainty affecting a linear system [2, 5] However, this generality has recently led to the somehow disappointing conclusion that most of the stability analysis problems involving polytopic uncertainty cannot be solved efficiently [7]. The aim of the authors in [25] was then to show that sufficient robust stability conditions can however be derived through special relaxation techniques based on parameter dependent Lyapunov functions [39] These conditions are expressed as convex LMI problems, whereas the original necessary and ....

V. D. Blondel, J. N. Tsitsiklis "A Survey of Computational Complexity Results in Systems and Control", to appear in Automatica, 2000.

....long horizon unobservable or fully observable any policy type NL NP PSPACE partially observable stationary NP NP NEXP time dependent NL NP PSPACE history dependent NL NP PSPACE Fig. 1. Summary of complexity results Complexity of Finite Horizon Markov Decision Process Problems Delta 11 Blondel and Tsitsiklis [1998] article, discusses both the complexity of algorithms and of the underlying problems, but the section on POMDPs does not go into the level of detail provided here. The following Section 2 presents a short overview of the complexity classes we use, and gives the formal definitions of ....

Blondel, V. and Tsitsiklis, J. 1998. A survey of computational complexity results in systems and control. Available from http://web.mit.edu/jnt/www/publ.html or http://web.mit.edu/~jnt/survey.ps. (postscript, 785K), to appear in Automatica.

.... For example, it was proved that checking robust stability of a polytope of polynomial matrices (the so called polytopic uncertainty model, see e.g. 2] is an NP hard problem even in the simple case that all vertex matrices are of degree zero (i.e. when they do not depend in the indeterminate) [4]. NP hardness roughly means that it is very unlikely to find an algorithm that solves the problem in a time which is a polynomial function of the problem dimensions. These negative results have naturally led to the development of conservative, yet tractable, polynomial time conditions for checking ....

V. D. Blondel, J. N. Tsitsiklis "A Survey of Computational Complexity Results in Systems and Control", to appear in Automatica, 2000. 13

....horizon long horizon unobservable or fully observable any policy type NL NP PSPACE partially observable stationary NP NP NEXP time dependent NL NP PSPACE history dependent NL NP PSPACE Fig. 1. Summary of complexity results Complexity of Finite Horizon Markov Decision Process Problems 11 Blondel and Tsitsiklis [1998] article, discusses both the complexity of algorithms and of the underlying problems, but the section on POMDPs does not go into the level of detail provided here. The following Section 2 presents a short overview of the complexity classes we use, and gives the formal de nitions of ....

Blondel, V. and Tsitsiklis, J. 1998. A survey of computational complexity results in systems and control. Available from http://web.mit.edu/jnt/www/publ.html or http://web.mit.edu/~jnt/survey.ps. (postscript, 785K), to appear in Automatica.

....of one coefficient that is allowed to vary within its interval. Based on this result, it was then shown that stability of an affine polynomial family can be checked efficiently with a polynomial time algorithm [26] As pointed out by Blondel and Tsitsiklis in their interesting recent survey [7], the problem of deciding whether a given family of polynomials is stable is equivalent to the problem of deciding whether the family contains an unstable polynomial. This is an analysis problem. As previously stated, in the case of interval and affine polynomial families, this analysis problem ....

V. D. Blondel and J. N. Tsitsiklis, "A Survey of Computational Complexity Results in Systems and Control", Institute of Mathematics, University of Li`ege, Belgium. Submitted for publication, 1998.

.... uncertainty is probably the most general representation of the parametric uncertainty affecting a linear system [2, 3] However, this generality has recently led to the somehow disappointing conclusion that most of the stability analysis problems involving polytopic uncertainty are NP hard [4]. Following the hierarchy described in [2] we now briefly review these results. In increasing order of complexity, we can distinguish between stability of ffl Interval polynomials, where each coefficient of the polynomial varies independently in a given interval. Kharitonov showed that stability ....

....of the polynomial varies independently in a given interval. Kharitonov showed that stability of an interval family of continuous time polynomials can be checked efficiently in polynomial time [2, 3] Unfortunately, there is no broad generalization of Kharitonov s result to other stability regions [4]. ffl Polytopes of polynomials, sometimes also referred to as affine polynomial families, which are linear combinations of a set of given polynomials. These families have value sets which are convex polygons in the complex plane. The Edge Theorem and polynomial time algorithms for checking ....

[Article contains additional citation context not shown here]

V. D. Blondel and J. N. Tsitsiklis, "A Survey of Computational Complexity Results in Systems and Control", Research Report, Institute of Mathematics, University of Li`ege, Belgium, October 1998. Submitted for publication.

....planning and stochastic control problems, and no computability results have previously been established for probabilistic planning. The undecidability of finding an optimal policy for an infinite horizon POMDP has been a matter of conjecture (Papadimitriou Tsitsiklis 1987) Littman 1996) (Blondel Tsitsiklis 1998). Our results settle these open problems and complement the research on the computational complexity of finitehorizon POMDP problems (Papadimitriou Tsitsiklis 1987; Littman 1996; Mundhenk, Goldsmith, Allender 1997; Littman, Goldsmith, Mundhenk 1998) We show that the following basic ....

Blondel, V. D., and Tsitsiklis, J. N. 1998. A survey of computational complexity results in systems and control. Submitted to Automatica, 1998.

No context found.

Vincent D. Blondel and John N. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36(9):1249--1274, 2000. 186 References

No context found.

V. D. Blondel and J. N. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36:9, pp. 1249-1274, 2000.

....Technical and Cultural A#airs. periodic switching functions converge to the origin. The problems of determining if a given switched system is absolutely or periodically stable are both computationally intractable (NP hard; see [18] It is yet unknown whether these problems are decidable, see [4] for a discussion of this issue. The related problem of determining if all trajectories of a switched linear system are bounded is known to be undecidable [5] For a discussion of various other issues related to switched linear systems ; see [1] 14] 15] Absolute stability clearly implies ....

.... This quantity was introduced in [7] see [8] for a corrigendum addendum) The generalized spectral radius is known to coincide (see [2] with the earlier defined joint spectral radius [16] the notion appears in a wide range of contexts and has led to a number of recent contributions (see, e.g. [4, 5, 9, 8, 12, 18, 19, 20]) a list of over hundred related contributions is given in [17] It is known that #(#) for all k 0. According to the finiteness conjecture, equality in this expression is always obtained for some finite k. The existence of a counterexample to the conjecture is proved in [6] by using ....

V. D. Blondel and J. N. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36:9, pp. 1249-1274, 2000.

.... # t (#) and # t (#) until they get su#ciently close) but unless P = NP, there is no polynomial time approximation algorithm [24] From this it follows that the problems of deciding whether #(#)61 or whether #(#) 1 are NP hard; see [20,10] as well as [9] for other relevant results; see also [4] for a general discussion. Let us also note the #niteness conjecture (FC) which states that ## #t such that # t (#) #(#) The #niteness conjecture is discussed by Lagarias and Wang [13] who note that if the FC is true, then the problem of determining whether #(#) 1 is decidable. This is ....

V.D. Blondel, J.N. Tsitsiklis, A survey of computational complexity results in systems and control, Automatica 36(9) (2000) 1249--1274

....whose dynamics are event driven. Such systems appear in a wide range of practical situations and there are a large number of papers on the computational complexity of discrete event systems that address issues such as minimal realization [7] reachability [15] and stability [4,28] see also [30] for a survey. In general, models that describe the behavior of discrete event systems are nonlinear but there is a class of discrete event systems for which the model becomes linear when formulated in the max plus semiring, see [1] for more details. In the context of these systems, the minimal ....

V.D. Blondel, J.N. Tsitsiklis, A survey of computational complexity results in systems and control, Automatica 36 (9) (2000) 1249--1274.

....[3] but for the case of discontinuous piecewise a#ne systems. The additional requirement of continuity imposed in this paper is a severe restriction, and makes undecidability much harder to establish. Surveys of decidability and complexity results for dynamical systems are given in [1] 12] and [7]. Our main result (Theorem 1) is a proof of Sontag s conjecture [6, 19] that global asymptotic stability of saturated linear systems is not decidable. Saturated linear systems are systems of the form x t 1 = #(Ax t ) where x t evolves in the state space R , A is a square matrix, and # denotes ....

V. D. Blondel and J. N. Tsitsiklis. A survey of computational complexity results in systems and control. To appear in Automatica, 1999.

....appears in a number of di#erent contexts. They are used to study Arthur and Merlin games [BaM88] CHPW98] space bounded interactive proofs [CL89] rational series and semigroups of matrices [BT00a] and Markov decision processes and planning questions [Bly99] MHC99] PT87] see Section 5 of [BT00b] for a survey) The results we prove here have implications for all problems that were proved undecidable by reduction from one of the problems we consider. In particular, using a reduction that appears in [BT00a] we prove as a corol 1 The author of [MHC99] does not seem to be aware of the ....

V. D. Blondel and J. N. Tsitsiklis. A Survey of Computational Complexity Results in Systems and Control. Automatica, 36(9):1249-1274, 2000.

....if trajectories associated to periodic switching functions converge to the origin. The problems of determining if a given switched system is absolutely or periodically stable are both computationally intractable (NP hard; see [18] It is yet unknown whether these problems are decidable, see [4] for a discussion of this issue. The related problem of determining if all trajectories of a switched linear system are bounded is known to be undecidable [5] For a discussion of various other issues related to switched linear systems 1 ; see [1] 14] 15] Absolute stability clearly implies ....

.... This quantity was introduced in [7] see [8] for a corrigendum addendum) The generalized spectral radius is known to coincide (see [2] with the earlier defined joint spectral radius [16] the notion appears in a wide range of contexts and has led to a number of recent contributions (see, e.g. [4, 5, 9, 8, 12, 18, 19, 20]) a list of over hundred related contributions is given in [17] It is known that #(#) # max #(A 1 A k ) 1 k : A i # #, i = 1, k for all k # 0. According to the finiteness conjecture, equality in this expression is always obtained for some finite k. The existence of a ....

V. D. Blondel and J. N. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36:9, pp. 1249-1274, 2000.

....radius is known to coincide (see [1] with the earlier defined joint spectral radius [12] we refer to these quantities simply as spectral radius . The notion of spectral radius of a set of matrices appears in a wide range of contexts and has led to a number of recent contributions (see, e.g. [2, 3, 5, 7, 10, 14, 15, 16]) a list of over hundred related contributions is given in [13] We describe below one particular occurrence in a dynamical system context. We consider systems of the form x t 1 = A t x t , where # is a finite set of matrices, and A t # # for every t # 0. We do not impose any restrictions on ....

V. D. Blondel and J. N. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36:9, pp. 1249-1274, 2000.

....[5] but for the case of discontinuous piecewise a#ne systems. The additional requirement of continuity imposed in this paper is a severe restriction, and makes undecidability much harder to establish. Surveys of decidability and complexity results for dynamical systems are given in [1] 15] and [9]. Our main result (Theorem 2.1) is a proof of Sontag s conjecture [8, 22] that global asymptotic stability of saturated linear systems is not decidable. Saturated linear systems are systems of the form x t 1 = #(Ax t ) where x t evolves in the state space R n , A is a square matrix, and # ....

V. D. Blondel and J. N. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36(9), 1249--1274, 2000.

.... there is no polynomial time approximation algorithm [Tsitsiklis and Blondel, 1997] From this it follows that the problems of deciding whether ae( Sigma) 1 or whether ae( Sigma) 1 are NP hard; see [Toker, 1997] and [Gurvits, 1996] as well as [Gurvits, 1995] for other relevant results; see also [Blondel and Tsitsiklis, 2000] for a general discussion. Let us also note the finiteness conjecture (FC) which states that 8 Sigma 9t such that ae t ( Sigma) ae( Sigma) The finiteness conjecture is discussed by Lagarias and Wang (1995) who note that if the FC is true, then the problem of determining whether ae( Sigma) ....

Blondel, V. D. and J. N. Tsitsiklis (2000). A survey of computational complexity results in systems and control, to appear in Automatica.

....[3] but for the case of discontinuous piecewise a#ne systems. The additional requirement of continuity imposed in this paper is a severe restriction, and makes undecidability much harder to establish. Surveys of decidability and complexity results for dynamical systems are given in [1] 12] and [7]. Our main result (Theorem 1) is a proof of Sontag s conjecture [6, 19] that global asymptotic stability of saturated linear systems is not decidable. Saturated linear systems are systems of the form x t 1 = #(Ax t ) where x t evolves in the state space R n , A is a square matrix, and # denotes ....

V. D. Blondel and J. N. Tsitsiklis. A survey of computational complexity results in systems and control. To appear in Automatica, 1999.

.... P = NP , there is no polynomial time approximation algorithm [Tsitsiklis and Blondel, 1997] From this it follows that the problems of deciding whether #(#) # 1 or whether #(#) 1 are NP hard; see [Toker, 1997] and [Gurvits, 1996] as well as [Gurvits, 1995] for other relevant results; see also [Blondel and Tsitsiklis, 2000] for a general discussion. Let us also note the finiteness conjecture (FC) which states that ## #t such that # t (#) #(#) The finiteness conjecture is discussed by Lagarias and Wang (1995) who note that if the FC is true, then the problem of determining whether #(#) 1 is decidable. This ....

Blondel, V. D. and J. N. Tsitsiklis (2000). A survey of computational complexity results in systems and control, to appear in Automatica.

....[3] but for the case of discontinuous piecewise a#ne systems. The additional requirement of continuity imposed in this paper is a severe restriction, and makes undecidability much harder to establish. Surveys of decidability and complexity results for dynamical systems are given in [1] 12] and [8]. Our main result (Theorem 1) is a proof of Sontag s conjecture [7, 19] that global asymptotic stability of saturated linear systems is not decidable. Saturated linear systems are systems of the form x t 1 = #(Ax t ) where x t evolves in the state space R n , A is a square matrix, and # denotes ....

V. D. Blondel and J. N. Tsitsiklis. A survey of computational complexity results in systems and control. To appear in Automatica, 1999.

....[3] but for the case of discontinuous piecewise a ne systems. The additional requirement of continuity imposed in this paper is a severe restriction, and makes undecidability much harder to establish. Surveys of decidability and complexity results for dynamical systems are given in [1] 12] and [7]. Our main result (Theorem 1) is a proof of Sontag s conjecture [6, 19] that global asymptotic stability of saturated linear systems is not decidable. Saturated linear systems are systems of the form x t 1 = Ax t ) where x t evolves in the state space R n , A is a square matrix, and denotes ....

V. D. Blondel and J. N. Tsitsiklis. A survey of computational complexity results in systems and control. To appear in Automatica, 1999.

No context found.

V.D. Blondel and J.N. Tsitsiklis, A survey of computational complexity results in systems and control, Automatica, 36, 9 (2000), 1249--1274.

No context found.

V. Blondel and J. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36, 2000, 1249-1274

No context found.

V. Blondel and J. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36, 2000, 1249-1274

No context found.

Vincent D. Blondel and John N. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36(9):1249--1274, 2000.

No context found.

Blondel, V. D. and Tsitsiklis, J. N. (2000). A survey of computational complexity results in systems and control. Automatica, 36(9):1249--1274.

No context found.

Blondel, V., and Tsitsiklis, J. A survey of computational complexity results in systems and control. Automatica 36 (2000), 1249--1274.

No context found.

Blondel, V. D. and J. N. Tsitsiklis (2000). "A Survey of Computational Complexity Results in Systems and Control," Automatica, vol. 36, pp. 1249-1274.

No context found.

V. D. Blondel and J. N. Tsitsiklis, "A survey of computational complexity results in systems and control," Automatica, vol. 36, no. 9, pp. 1249--1274, 2000.

No context found.

V. D. Blondel and J. N. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36:1249--1274, 2000.

No context found.

V. D. Blondel and J. N. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36:1249--1274, 2000.

No context found.

V. D. Blondel and J. N. Tsitsiklis, A survey of computational complexity results in systems and control, Automatica, 36 (2000), pp. 1249-1274.

No context found.

Vincent D. Blondel and John N. Tsitsiklis. A survey of computational complexity results in systems and control. Automatica, 36(9):1249--1274, 2000.

No context found.

V. D. Blondel and J. N. Tsitsiklis. A Survey of Computational Complexity Results in Systems and Control. Automatica, Vol. 36, pp. 1249--1274, 2000.

No context found.

Blondel, V. D. and J. N. Tsitsiklis (1999). "A Survey on Computational Complexity Results in Systems and Control," to appear.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC