C. A. Desoer and M. A. Vidyasagar, Feedback Systems: Input-Output Properties, Academic Press, 1975.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... have played a prominent role in systems and control theory and have led to a number of important stability criteria for unity feedback controls applied to linear dynamical systems subject to static input or output nonlinearities, see [1, 8, 9, 10, 11, 16, 20, 25, 30] for the nitedimensional and [2, 3, 4, 5, 7, 11, 12, 15, 20, 25, 28, 29] for the in nite dimensional case, to mention just a few references. j r u R r Figure 1 In this paper we study an absolute stability problem for the feedback system shown in Figure 1. The input output operator G is linear, shift invariant and bounded from (R ; U) into ....

C.A. Desoer and M. Vidyasagar. Feedback Systems: Input-Output Properties, Academic Press, New York, 1975.

....function. Proof. We have: 1 ) 2] clear by Definitions) 2 ) 3] see Lemma 4.9) 3 ) 4] see Lemma 4.8) 4 ) 1] see Lemma 4.5) 4. 5 Remarks about Gain Functions As it is well recognized in the literature, the notion of iss is a natural nonlinear extension of classical finite gain stability [5] in that only linear incremental gains are considered. That is why we refer fl in the iss property (29) as an iss gain. Naturally, we raise the question of how to compute such a gain function for a given iss system (28) As in the continuous time case [27] a similar iss algorithm can be ....

C. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties. Academic Press, New York, 1975.

.... conditions have played a prominent role in systems and control theory and have led to a number of important stability criteria for unity feedback controls applied to linear dynamical systems subject to static input or output nonlinearities, see [1, 13, 14, 23, 34, 39] for the nite dimensional and [2, 6, 9, 18, 22, 34, 37] for the in nite dimensional case, to mention just a few references. r Figure 1 In this paper we study an absolute stability problem for the feedback system shown in Figure 1. The input output operator G is linear, shift invariant and bounded from (R ; U) into itself and : U ....

....references therein. In the in nite dimensional case the literature on absolute stability problems is dominated by input output approaches, see, for example, 8] which gives the rst treatment of the Popov criterion in a distributed parameter context, and see the relevant chapters in the books [4, 9, 16, 21, 22, 28, 34] and the references therein. The number of absolute stability results in an in nite dimensional state space setting is fairly limited (see [2, 3, 6, 11, 17, 18, 37, 38] Some of these references, namely [3, 4, 38] and parts of [16] see also the forthcoming paper [5] by the authors) consider ....

[Article contains additional citation context not shown here]

C.A. Desoer and M. Vidyasagar. Feedback Systems: Input-Output Properties, Academic Press, New York, 1975.

.... Delta 0 as i 1. From the identity M i ;N = I Gamma Phi i Phi i Sigma M i ;N we see that k Sigma M i ;N k Delta 0. 2 Notes 1. The small gain theorem was introduced as an analysis tool for studying the stability of interconnected dynamical systems (cf. 19] 12] [2]) The theorem applies to the feedback configuration of Fig. 1 under the assumption that P and C are stable. The precise statement is: if kPk Delta :kCk Delta 1 then the feedback system of Fig. 1. is stable. This result, together with bounds for kHP;C k Delta (cf. 19] 2] can be derived ....

....(cf. 19] 12] 2] The theorem applies to the feedback configuration of Fig. 1 under the assumption that P and C are stable. The precise statement is: if kPk Delta :kCk Delta 1 then the feedback system of Fig. 1. is stable. This result, together with bounds for kHP;C k Delta (cf. 19] [2]) can be derived from the basic lemma stated in the text. 2. The gap metric was introduced into the control literature by G. Zames and A.K. El Sakkary [21] as an analysis tool for studying perturbations of dynamical systems, and for assessing the robustness of stability of feedback ....

C.A. Desoer and M. Vidyasagar, Feedback systems: Input-output properties, Academic Press: New York, 1975.

....t## Fm (t) F e (t) 0. In the case where there is a time delay in the communication network, it should be incorporated in the designing method such that the previous objectives still maintain. An approach used to solve the above problem is based on the passivity and scattering theory [1]: if the input power flow does not exceed the output power flow for a given system, then the input output stability of the system is guaranteed. In this context, a bilateral teleoperation system shown in Figure 1 would be represented as a network of resistors, inductors and capacitors as shown in ....

C. A. Desoer and M. Vidyasagar, Feedback systems: Input-Output properties. New York: Academic Press, 1975.

....=0 for k = r 1, n. Since, # k 0 (statement 1) it follows that # r 1 = # n =0. 3. Since M is linear and since S n consists of one dimensional subspaces of we have that # n =inf 0#=x#X Mx#p #x#p is strictly larger than zero if M has rank n. 4. It is shown in the Appendix C.2. 16 of [1] that #M# # ind ##M# p ind .Thisisequivalent to # 1 . 3 Problem formulations In this section we consider a number of problems where the p norm induced singular values play a natural role. 3.1 Rank deficiency An important application of singular values stems from the numerical di#culty ....

C.A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties.,Academic Press, London, 1975.

....systems, H # (C ) transfer functions induce stability, i.e. bounded L inputs bounded L outputs correspondence on one hand, and exponential stability of the internal minimal realization on the other. The former property remains intact for infinitedimensional systems (Desoer and Vidyasagar [1975]) and there are in fact a number of investigations on robust stability stabilizability along this line (Chen and Desoer [1982] Curtain and Glover [1986] Khargonekar and Poola [1986] just to name a few) On the other hand, there arises a problem in dealing with exponential stability of ....

....on robust stability stabilizability along this line (Chen and Desoer [1982] Curtain and Glover [1986] Khargonekar and Poola [1986] just to name a few) On the other hand, there arises a problem in dealing with exponential stability of infinite dimensional systems. For example, Zabczyk [1975] gave an example of a system in which the spectrum is contained in the half plane # c , c 0, yet its states grow as fast as e . More recently, Logemann [1987] gave an example of a transfer function of a neutral delay di#erential system whose transfer function belongs to H # (C ) and yet ....

[Article contains additional citation context not shown here]

C. A. Desoer and M. Vidyasagar, Feedback Systems: Input/Output Properties, Academic Press, 1975.

....random walk directly on the coefficients, that is (4) A model of this form is not constrained to be stable, which is an undesirable feature for audio. For sufficiently slow parameter variation, the stability criterion of a TVAR system is the same as for the time invariant one (see, for example, [22]) that is, stability is enforced by ensuring that all the instantaneous poles of the TVAR model, or the roots of the polynomial lie strictly within the unit circle. This form of model was employed in the fixed lag filtering work of [23] As an alternative to direct coefficient modeling, one can ....

C. A. Desoer and M. Vidyasagar, Feedback Systems: Input--Output Properties. New York: Academic, 1976.

....Let us start with some simple stability analysis. Suppose for simplicity that P (s) is stable. An easy loop transformation converts Fig. 4 to Fig. 5. By the stability of P (s) we have neglected the initial value responses. A straightforward application of the small gain theorem (e.g. [16]) yields e Ls )r(s) e(s) Figure 5: Equivalent System that the converted system is L input output stable if #1 P## 1, 3) 8 where ## # denotes the standard H # norm (1) Several problems arise: Condition (3) is only a su#cient condition. How close is it to ....

.... if we further assume some sort of regularity assumption on the transfer function, then the usual small gain condition (e.g. 10] implies internal exponential stability also [62] This means that for a restricted class of systems, H # transfer functions yield not only L input output stability [16] but internal stability also (see, e.g. 37] for related issues) This is applicable to modified repetitive control systems. Consider the modified repetitive control system with plant perturbation # given in Fig. 8. Assume for simplicity that P (s) and C(s) are stable. As established in Section ....

C. A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties, Academic Press, 1975.

.... storage E(0) is passive if and only if, t (f 1 (#) v 1 (#) f M (#) v M (#) d# E (0) 0, #t # 0 (1) for all admissible forces (f 1 , f M ) and velocities (v 1 , v M ) Equation (1) states that the energy applied to a passive network must exceed E(0) for all time[20] [29]. In haptic interface systems, the relevant forces and velocities can be measured by the computer and (1) can be computed in real time by appropriate software. This software is very simple in principle because at each time step, 1) can be evaluated with few mathematical operations. 2.1 ....

Desoer, C. A., and Vidyasagar, M., Feedback Systems: Input-Output Properties, New York: Academic, 1975. 24

.... Let (1) denote the matrix measure induced by some vector or matrix norm and defined by the formula (A) lim #0 jjI Ajj : The matrix measure induced by the 2 norm (i.e. the Euclidean norm) is denoted by 2 (A) and 2 (A) Properties of the matrix measure can be found in [11] and [12]. Lemma 2.1: For any matrix A and any symmetric matrix B[6] let A = A A ) 2, then we have n(A)tr(B)0 n(B) nn(A) tr (AB) 1(A)tr(B)0 n(B) 1(n1(A) 0 tr (A) In particular, for any positive semidefinite matrix B we have n(A)tr(B)tr (AB) 1 (A)tr(B) Lemma 2.2: Let F (1) denote the ....

C. A. Desoer and M. Vidyasagar, Feedback Systems: Input--Output Properties. New York: Academic, 1975.

....question that arises with the feedback system in Fig. 1 is that of robust stability : Is the system stable for all possible instances of A This question can be partially answered using a number of approaches. For example, if the L2 gain of A does not exceed one, the small gain theorem [7] asserts that the system is robustly stable if the L2 gain (which is also the H norm) of P is less than one. And, if A is known to be passive, the passivity theorem [7] asserts that closed loop stability is ensured as long as P is strictly passive. If it is known further that A is block diagonal, ....

....be partially answered using a number of approaches. For example, if the L2 gain of A does not exceed one, the small gain theorem [7] asserts that the system is robustly stable if the L2 gain (which is also the H norm) of P is less than one. And, if A is known to be passive, the passivity theorem [7] asserts that closed loop stability is ensured as long as P is strictly passive. If it is known further that A is block diagonal, then it is enough that an appropriately scaled version of P have L2 gaJn less than one or be strictly passive, respectively. Necessary and sufficient conditions in this ....

C. A. Desoer and M. Vidyasagar. Feedback Systems: Input-Output Properties. Academic Press, New York, 1975.

....Hilbert spaces, L p spaces, the Laplace and Fourier transforms, some facts from matrix theory, and finally some theorems on complex functions including the Nyquist stability criterion. Much of the material presented in this Chapter can also be found in various textbooks, we especially mention [Vid93, Wei91, DV75]. 2.1 Normed spaces and inner products Definition 1 (Linear vector space) A linear vector space (V, K) is a set V over a field K (typically R or C) and two operations, the addition : V V and a scalar multiplication : K V. We assume that the usual axioms for addition and ....

....equation) The following two statements are equivalent: i) Re [# i (A) 0 for all i; ii) there exists a positive definite matrix P = P such that PA A # P is negative definite. 2.4. 3 The matrix measure The material about matrix measures can be found for instance in Desoer Vidyasagar [DV75] and Fang Kincaid [FK96] Definition 20. Let some matrix norm induced by an vector norm in the complex space. Then the limit (A) lim ##0 #I #A# (2.34) is well defined and is called the measure of the matrix A. Note that the measure (A) depends on the vector norm inducing ....

[Article contains additional citation context not shown here]

C. Desoer and M. Vidyasagar. Feedback Systems: input-output properties. Academic Press, New York, 1975. 2, 2.4.3, 2.5, 3.2, 3.5.1, 4.3, 4.3

....to large peaking in the system frequency response. D. Circle Criterion Constraint The reader may have recognized the minimum loop margin constraint (32) of the previous section as a special form of the circle criterion due to Zames [62] Sandberg [63] and Narendra and Goldwyn [64] see also [65] [68] The circle criterion requires the loop gain to remain outside a forbidden circle in the complex plane; if the circle is centered at the critical point 1 and has radius M, this is the loop margin constraint (32) The circle criterion provides a sufficient condition for closed loop ....

C.A. Desoer and M. Vidyasagar, Feedback Systems: Input- Output Properties. New York, NY: Academic Press, 1975.

No context found.

C. A. Desoer and M. Vidyasagar, Feedback Systems: Input/Output Properties, Academic Press, 1975.

No context found.

C. A. Desoer and M. A. Vidyasagar, Feedback Systems: Input-Output Properties, Academic Press, 1975.

No context found.

C. A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties, Academic Press, New York, #1975#.

No context found.

C. A. Desoer and M. Vidyasagar. Feedback systems: Input-Output properties.Academic Press. New York, N.Y., #975.

No context found.

C. A. Desoer and M. Vidyasagar, Feedback systems: Inputoutput properties, Academic Press, 1976.

No context found.

C. A. Desoer and M. Vidyasagar. Feedback Systems: Input-Output Properties. Academic Press, New York, 1975.

No context found.

C.A. DESOER and M. VIDYASAGAR. Feedback Systems: Input-Output Properties. Academic Press, New York, 1975.

No context found.

C. A. Desoer and M. Vidyasagar. Feedback Systems: Input-Output Properties. Academic Press, New York, 1975.

No context found.

C.A. Desoer and M. Vidyasagar. Feedback Systems: Input-Output Properties. Academic Press, 1975.

No context found.

Desoer, C. A., and Vidyasagar, M., Feedback Systems: Input-Output Properties, Academic Press, New York, NY, 1975.

No context found.

C. A. Desoer and M. Vidyasagar. Feedback Systems: Input-Output Properties, Academic Press, New York, 1975.

First 50 documents  Next 50

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