Robustness of linear quadratic state feedback designs in the presence of system uncertainty

Patel, R.V.; Toda, Mikito; Sridhar, B.

doi:10.1109/tac.1977.1101658

Cited by 158 publications

(21 citation statements)

References 7 publications

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“…Furthermore, Theorem 2 provides an extension in optimal control concepts. Both Corollaries I and 2 also extend the results of Patel et al (1977) to the large-scale systems. Since these results have the forms of algebraic criteria, we can estimate the perturbation bounds in advance when we design a system.…”

Section: Resultssupporting

confidence: 70%

Robustness of perturbed large-scale systems with local constant state feedback

Wang

Cheng

1989

International Journal of Control

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The robustness problem of perturbed large-scalesystems is considered. The nominal large-scale system is stabilized by a local constant state feedback u,(t) = k,Xi(t) and the local optimal control law ui(t) = -R i -I BJ PiXi(t), respectively. In the above two cases, bounds are obtained for an allowable non-linear time-invariant (or timevarying) perturbation such that the resulting closed-loop large-scale system remains stable. The special case of a linear perturbation is also treated here. Nomenclature IR n real vector space of dimension n AT transpose of the matrix A A i ( A) ith eigenvalue of the matrix A II A lis spectral norm of the matrix A i.e. IIA lis = max [)'i(A T A)]112 , ( m )112 i.e. Ilgll = J,lgil 2 ,

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Section: Resultssupporting

confidence: 70%

Robustness of perturbed large-scale systems with local constant state feedback

Wang

Cheng

1989

International Journal of Control

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“…9) O=(A+AA)QaA+Qaa(A+AA)r+ V. Now subtracting (1.9) from (1.6) yields 0 (A + AA )( Q-QAA) 4r Q-Qaa)(A + AA r + f(Q)_( AAQ + QAA r) + V, which, by (1.7) and the fact that A + AA is stable, implies (1. 10) QA<-Q. Now 1.5 and (1.10) yield the bound (1.8).…”

mentioning

confidence: 84%

Robust Stability and Performance Analysis for State-Space Systems via Quadratic Lyapunov Bounds

Bernstein¹,

Haddad²

1990

SIAM J. Matrix Anal. & Appl.

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Abstract. For a given asymptotically stable linear dynamic system it is often of interest to determine whether stability is preserved as the system varies within a specified class of uncertainties. If, in addition, there also exist associated performance measures (such as the steady-state variances of selected state variables), it is desirable to assess the worst-case performance over a class of plant variations. These are problems of robust stability and performance analysis. In the present paper, quadratic Lyapunov bounds used to obtain a simultaneous treatment of both robust stability and performance are considered. The approach is based on the construction of modified Lyapunov equations, which provide sufficient conditions for robust stability along with robust performance bounds. In this paper, a wide variety of quadratic Lyapunov bounds are systematically developed and a unified treatment of several bounds developed previously for feedback control design is provided.

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“…In [3], Xu and Liu propose an improved Razumikhin-type theorem and show that less conservative bounds than those of Cheres et al [2] can be obtained. Furthermore, the bounds derived in [3] are the same as those derived in [5] and [6] for nondelayed unstructured perturbations.…”

Section: Introductionmentioning

confidence: 99%

On robustness and stabilization of linear systems with delayed nonlinear perturbations

Trinh

Aldeen²

1997

IEEE Trans. Automat. Contr.

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In this paper, by employing a Razumikhin-type theorem, a robust stability criterion for a class of linear systems subject to delayed time-varying nonlinear perturbations is given. Then, stabilization of a class of linear systems subject to mismatched delayed time-varying nonlinear perturbations by linear controller is considered. For such systems, conditions which ensure closed-loop asymptotic stability are given. Numerical examples are given to illustrate the results. NOMENCLATURE R Real number space, R = (01; 1); R + = [0; 1);J = [; 1), where 2 R. R n Real vector space of dimension n: R n2m

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Robustness of linear quadratic state feedback designs in the presence of system uncertainty

Cited by 158 publications

References 7 publications

Robustness of perturbed large-scale systems with local constant state feedback

Robustness of perturbed large-scale systems with local constant state feedback

Robust Stability and Performance Analysis for State-Space Systems via Quadratic Lyapunov Bounds

On robustness and stabilization of linear systems with delayed nonlinear perturbations

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