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Abstract: A wide variety of problems in systems and control theory can be cast or recast as convex problems that involve linear matrix inequalities (LMIs). For a few very special cases there are "analytical solutions" to these problems, but in general they can be solved numerically very efficiently. In many cases the inequalities have the form of simultaneous Lyapunov or algebraic Riccati inequalities; such problems can be solved in a time that is comparable to the time required to solve the same number... (Update)
Context of citations to this paper: More
.... discussed in this survey consider both the single input case (q = 1 in [1] 14] 18] and [19] and the multiple input case (q 1 in [6] and [9] In the former, the state control vector is k T = k 1 ; k 2 ; k n ] and in the latter, the control matrix is a q...
...more on eigenvalue optimization, see [37] 4. 3 Engineering Many early applications of SDP appeared in the Engineering literature, e.g. [11, 66, 65]. This was particularly evident in control theory, where it has emerged as an important practical tool for the analysis of...
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BibTeX entry: (Update)
S. BOYD, V. BALAKRISHNAN, E. FERON, and L. El GHAOUI. Control system analysis and synthesis via linear matrix inequalities. Proc. ACC, pages 2147--2154, 1993. http://citeseer.ist.psu.edu/boyd93control.html More
@article{ boyd93control,
author = "S. {BOYD} and V. {BALAKRISHNAN} and E. {FERON} and L. {El~{G}{HAOUI}}",
title = "Control system analysis and synthesis via linear matrix inequalities",
journal = "{Proc. ACC}",
pages = "2147--2154",
year = "1993",
url = "citeseer.ist.psu.edu/boyd93control.html" }
Citations (may not include all citations):529 Linear matrix inequalities in systems and control theory (context) - Boyd, Ghaoui et al. - 1993
307 Interior point polynomial methods in convex programming: The.. (context) - Nesterov, Nemirovsky - 1993
113 Optimal Control: Linear Quadratic Methods (context) - Anderson, Moore - 1990
97 Analysis of feedback systems with structured uncertainties (context) - Doyle - 1982
90 Primal-dual potential reduction method for problems involvin.. - Vandenberghe, Boyd - 1993
83 Linear Controller Design: Limits of Performance (context) - Boyd, Barratt - 1991
77 Gain scheduling via linear fractional transformations (context) - Packard - 1993
68 Robustness in the presence of mixed parametric uncertainty a.. (context) - Fan, Tits et al. - 1991
66 Method of centers for minimizing generalized eigenvalues - Boyd, Ghaoui - 1993
51 Least squares stationary optimal control and the algebraic R.. (context) - Willems - 1971
47 On minimizing the maximum eigenvalue of a symmetric matrix (context) - Overton - 1988
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29 The minimization of certain nondifferentiable sums of eigenv.. (context) - Cullum, Donath et al. - 1975
28 The Analysis of Feedback Systems (context) - Willems - 1971
28 A collection of robust control problems leading to LMI's (context) - Packard, Zhou et al. - 1991
27 Stability margins of diagonally perturbed multivariable feed.. (context) - Safonov - 1982
23 Estimation and Filtering Problems: Accuracy Aspects (context) - Gevers, Li et al. - 1993
20 Robust stabilization of uncertain linear systems: quadratic .. (context) - Khargonekar, Petersen et al. - 1990
17 Structured and simultaneous Lyapunov functions for system st.. - Boyd, Yang - 1989
17 control: a convex optimization approach (context) - Khargonekar, Rotea - 1991
16 An interior point method for generalized linear-fractional p.. (context) - Nesterov, Nemirovsky - 1991
12 A linear programming oriented procedure for quadratic stabil.. (context) - Bernussou, Peres et al. - 1989
12 Optimization over the positive semi-definite cone : Interior.. (context) - Alizadeh - 1992
11 Real Km - synthesis via generalized popov multipliers (context) - Chiang, Safonov - 1992
8 Extensions of mixed- bounds to monotonic and odd monotonic n.. (context) - Haddad, How et al. - 1992
8 When is a linear control system optimal (context) - Kalman - 1964
8 The method of matrix inequalities in the stability theory of.. (context) - Yakubovich - 1967
7 Stabilization of uncertain systems with norm bounded uncerta.. (context) - Khargonekar, Rotea - 1988
6 Computing bounds for the structured singular value via an in.. - Balakrishnan, Feron et al. - 1992
6 Quadratic stability with real and complex perturbations (context) - Packard, Doyle - 1990
6 A hybrid algorithm for optimizing eigenvalues of symmetric d.. (context) - Haeberly, Overton - 1993
6 complex Km -synthesis without curve fitting (context) - Safonov, Chiang - 1993
5 Solution of certain matrix inequalities encountered in nonli.. (context) - Yakubovich - 1964
5 control for linear systems with norm-bounded time-varying un.. (context) - Xie, de Souza - 1992
5 eme g'en'eral de la stabilit 'e du mouvement (context) - Lyapunov - 1947
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4 On minimizing the largest eigenvalue of a symmetric matrix (context) - Fan, Nekooie - 1992
4 Absolute stability and absolute instability of control syste.. (context) - Kamenetskii - 1983
4 A quadratically convergent algorithm on minimizing the large.. (context) - Fan - 1992
3 Robust stabilization of linear systems with norm-bounded tim.. (context) - Zhou, Khargonekar - 1988
3 An interior--point method for minimizing the largest eigenva.. (context) - Jarre - 1991
3 time invariant plants with uncertain parameters (context) - Horisberger, Belanger et al. - 1976
3 Computeraided stability criterion renders Popov criterion ob.. (context) - Safonov, Wyetzner - 1987
2 Minimizing conservativeness of robust singular values (context) - Safonov, Doyle - 1984
2 Quadratic stabilization and robust disturbance attenuation u.. (context) - Ohara, Souda et al. - 1992
1 Quadratic stabilizability of uncertain linear systems: exist.. (context) - Petersen - 1985
1 Optimal quadratic stabilizability of uncertain linear system.. (context) - Hollot, Barmish - 1980
1 Fixed point digital filters (context) - Mullis, Roberts - 1976
1 Gain-scheduled state-feedback with quadratic stability for u.. (context) - Becker, Packard - 1991
1 of Circuit Theory and Applications (context) - Thiele, discrete et al. - 1984
1 Bound invariant Lyapunov functions: a means for enlarging th.. (context) - Hollot - 1987
1 Linear feedback stabilization of arbitrary time-varying unce.. (context) - Gu - 1992
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