∞ guaranteed cost control for uncertain continuous-time linear systems

Peres, Pedro L. D.; Geromel, J.C.; Souza, Sérgio Ricardo de

doi:10.1016/0167-6911(93)90102-c

Cited by 50 publications

(25 citation statements)

References 15 publications

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“…Here, we will show proof of stability for (10). Since the properties of regular and impulse free can be easily proven using the Theorem 1 procedure outlined in [17], we omit the procedure.…”

Section: Resultsmentioning

confidence: 98%

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Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays

Kim

2009

Int. J. Control Autom. Syst.

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This paper considers the design problems of a delay-dependent robust and non-fragile guaranteed cost controller for singular systems with parameter uncertainties and time-varying delays in state and control input. The designed controller, under the possibility of feedback gain variations, can guarantee that a closed-loop system is regular, impulse-free, stable, an upper bound of guaranteed cost function, and non-fragility in spite of parameter uncertainties, time-varying delays, and controller fragility. The existence condition of the controller, the controller's design method, the upper bound of guaranteed cost function, and the measure of non-fragility in the controller are proposed using the linear matrix inequality (LMI) technique. Finally, numerical examples are given to illustrate the effectiveness and less conservatism of the proposed design method.

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Section: Resultsmentioning

confidence: 98%

“…Since Chang and Peng [8], guaranteed cost control problems have been considered extensively [4,[8][9][10][11]. Although many results have been considered regarding guaranteed cost control design methods, most of the work has been focused on non-singular systems.…”

Section: Introductionmentioning

confidence: 99%

Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays

Kim

2009

Int. J. Control Autom. Syst.

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“…andα N is given by (3). From the feasibility of the conditions of Theorem 1 one has that M < 0, = 1,...,J(g + 1) at the corners of the hyper-rectangle D c given by equation (5), which is sufficient (based on convexity) to assure that (29) is negative definite for all α ∈ U and for all α ∈ D, thus implying that the closed-loop system (7)-(8) is asymptotically stable with an H ∞ guaranteed cost given by γ = √ µ , µ = min µ.…”

Section: Theorem 1 For a Given Set Of Bounds On The Rates Of Parametrmentioning

confidence: 99%

“…In the context of control design, the determination of a robust (fixed) state feedback gain that assures to the closed-loop system a prescribed H ∞ norm (for precisely known systems - [2]) or a prescribed H ∞ guaranteed cost (for uncertain systems - [3]) is also a relevant task. Lyapunov-based techniques can be applied to design fixed state feedback H ∞ control gains for linear systems affected by parametric uncertainty.…”

Section: Introductionmentioning

confidence: 99%

“…Lyapunov-based techniques can be applied to design fixed state feedback H ∞ control gains for linear systems affected by parametric uncertainty. In this case, the controller can be computed through a convex optimization problem with linear matrix inequality constraints (LMIs -see [4]), using, for instance, quadratic stability [3]. Although the use of a robust state feedback gain simplifies the implementation of the control law since it does not require the on-line availability of the time-varying parameters, there are some systems that do not admit a fixed quadratically stabilizing state feedback gain, or, which occurs quite frequently, the system admits a fixed quadratically stabilizing feedback control but this gain does not provide an adequate closed-loop H ∞ performance.…”

Section: Introductionmentioning

confidence: 99%

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Design of H<sub>∞</sub> Gain-Scheduled Controllers for Linear Time-Varying Systems by means of Polynomial Lyapunov Functions

Montagner

Oliveira

Peres

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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This paper proposes convex conditions to design parameter-dependent (i.e. gain-scheduled) state feedback controllers that ensure closed-loop stability with H ∞ performance for linear systems affected by time-varying parameters that belong to a polytope and have bounded time-derivatives. The conditions, based on homogeneous polynomially parameterdependent Lyapunov functions of arbitrary degree, are expressed as a set of linear matrix inequalities written in terms of the vertices of the polytope, the bounds on the rates of parametric variations and the degree of the Lyapunov function. Differently from other gain-scheduled strategies in the literature, all the system matrices here are supposed to be affected by time-varying parameters and the control gains are obtained from a finite dimension convex optimization problem, which avoids to cope with nonlinear matrix inequalities and does not require the use of gridding procedures in the space of the parameters. Numerical results illustrate the efficiency of the proposed conditions, providing progressively less conservative results as the degree of the Lyapunov function increases.

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Parameterized LMIs for robust and state feedback control of continuous‐time polytopic systems

Rodrigues

Oliveira

Camino

2017

Intl J Robust & Nonlinear

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Summary This paper presents new extended linear matrix inequality (LMI) characterizations for the synthesis of robust H∞ and H2 state feedback controllers for continuous‐time linear time‐invariant systems with polytopic uncertainty. Based on a suitable change of variables and the Elimination Lemma, the proposed robust control design techniques are stated as extended LMI conditions parameterized in terms of 2 scalar parameters. One parameter is shown to belong to a bounded domain, thus limiting the scalar search domain. For the other parameter, a bounded subset is provided from numerical experiments. The benefits of the methodology are illustrated through numerical simulations performed on an uncertain model borrowed from the literature. It is shown that the proposed LMI relaxations can provide less conservative results with fewer scalar searches than some existing methods in the literature.

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∞ guaranteed cost control for uncertain continuous-time linear systems

Cited by 50 publications

References 15 publications

Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays

Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays

Design of H<sub>∞</sub> Gain-Scheduled Controllers for Linear Time-Varying Systems by means of Polynomial Lyapunov Functions

Parameterized LMIs for robust and state feedback control of continuous‐time polytopic systems

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∞ guaranteed cost control for uncertain continuous-time linear systems

Cited by 50 publications

References 15 publications

Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays

Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays

Design of H<sub>&#x0221E;</sub> Gain-Scheduled Controllers for Linear Time-Varying Systems by means of Polynomial Lyapunov Functions

Parameterized LMIs for robust and state feedback control of continuous‐time polytopic systems

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Design of H<sub>∞</sub> Gain-Scheduled Controllers for Linear Time-Varying Systems by means of Polynomial Lyapunov Functions