ℋ<sub>2</sub>guaranteed cost control for uncertain discrete-time linear systems

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

doi:10.1080/00207179308934418

Cited by 48 publications

(22 citation statements)

References 7 publications

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“…as q = 1 it is independent on the parameter; as q = 2 it reduces to the gain scheduled control law in [7]. From Theorem 2 one can conclude less conservative results can be obtained by increasing q.…”

Section: Remark 1 Algorithm (29) Applies the Lyapunov Functionmentioning

confidence: 73%

“…For example as q = 0, it is the common Lyapunov function [4]; as q = 1 it reduces to the parameter-dependent Lyapunov function in [7]. In addition, algorithm (29) utilizes the more general control law…”

Section: Remark 1 Algorithm (29) Applies the Lyapunov Functionmentioning

confidence: 99%

“…Note, [7] utilizes the parameter-dependent Lyapunov function and gain scheduled control law to cope with the H ∞ problem of the polytopic system. The extension of the method in [7] to deal with polytopic systems with input saturation is straightforward.…”

Section: Remark 1 Algorithm (29) Applies the Lyapunov Functionmentioning

confidence: 99%

“…The extension of the method in [7] to deal with polytopic systems with input saturation is straightforward. Using the Lyapunov function and gain scheduled control law proposed in [7] and following the same line in algorithm (29), one gets the following algorithm (30)…”

Section: Remark 1 Algorithm (29) Applies the Lyapunov Functionmentioning

confidence: 99%

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Gain Scheduled State Feedback Control for Discrete-Time-Varying Polytopic Systems Subject to Input Saturation

Wang

Liu

2011

Circuits Syst Signal Process

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In this paper, we study the stability and performance optimization problem of discrete-time-varying polytopic systems with actuator saturation. First, the homogeneous polynomially parameter-dependent matrix function (HPP-DMF for abbreviation) is proposed. Then, a set invariance condition is obtained by applying the HPP-DMF to the Lyapunov function and gain scheduled control law. Based on the set invariance condition, an algorithm is proposed to minimize the worst-case performance. The conditions in the algorithm are expressed in terms of linear matrix inequalities (LMIs). In addition, it is shown that as the degree of the HPP-DMF increases the conditions become less conservative. A numerical example is presented to demonstrate the effectiveness and superiority of the proposed technique.

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Section: Remark 1 Algorithm (29) Applies the Lyapunov Functionmentioning

confidence: 73%

Section: Remark 1 Algorithm (29) Applies the Lyapunov Functionmentioning

confidence: 99%

Section: Remark 1 Algorithm (29) Applies the Lyapunov Functionmentioning

confidence: 99%

Section: Remark 1 Algorithm (29) Applies the Lyapunov Functionmentioning

confidence: 99%

See 2 more Smart Citations

Gain Scheduled State Feedback Control for Discrete-Time-Varying Polytopic Systems Subject to Input Saturation

Wang

Liu

2011

Circuits Syst Signal Process

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“…Nessa direção, resultados baseados na estabilidade quadrá-tica (Barmish, 1994) podem ser facilmente encontrados, alguns utilizando as normas H 2 e H ∞ como índices de desempenho (Geromel et al, 1993), (Khargonekar e Rotea, 1991). Entretanto, essa abordagem tende a fornecer resultados muito conservadores por utilizar uma única função de Lyapunov fixa para todo o domínio de incertezas do sistema.…”

Section: Introductionunclassified

Alocação robusta de pólos através de realimentação de estados dependente de parâmetros

Leite

Montagner

Peres

2004

Sba Controle & Automação

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A sufficient condition for the existence of a robust parameter dependent state feedback gain is presented. This condition is formulated as a feasibility test of a set of linear matrix inequalities. Moreover, the feedback gain assures to the uncertain closed-loop system a robust pole location inside a prespecified circular region in the complex plane, by means of a parameter dependent Lyapunov function. Examples illustrate the results. KEYWORDS:Robust pole placement, parameter dependent state feedback, parameter dependent Lyapunov function, linear matrix inequality, polytopic uncertainty. RESUMOUma condição suficiente para a existência de uma realimentação de estados robusta dependente de parâmetros é apresentada neste trabalho. A condição é verificada através do teste de factibilidade de um conjunto de desigualdades matriciais lineares. A realimentação obtida garante ainda a alocação robusta dos pólos de malha fechada de sistemas lineares incertos em uma região circular do plano complexo, através da existência de uma função de Lyapunov depenArtigo submetido em 12/04/02 1a. Revisão em 29/10/02, 2a. Revisão em 08/04/03 Aceito sob recomendação do Ed. Assoc. Prof. José R. C. Piqueira dente de parâmetros. Exemplos ilustram os resultados. PALAVRAS-CHAVE:Alocação robusta de pólos, realimentação de estados dependente de parâmetros, função de Lyapunov dependente de parâmetros, desigualdades matriciais lineares, incertezas politópicas. INTRODUÇÃOEm geral, os processos industriais sofrem ações de fatores externos como temperatura, umidade, pressão, ponto operacional, etc. Esses elementos afetam a dinâmica dos processos e precisam ser considerados no projeto de controladores. Outra situação bastante comum é a dos processos em batelada. Nesses casos, as condições operacionais podem ser completamente diferentes de uma execução para outra. Na maioria das vezes, essa relação entre os elementos que caracterizam a dinâmica do sistema e as condições operacionais do processo pode ser representada por modelos lineares com parâmetros incertos.Nas últimas décadas, algumas abordagens para a análise e projeto que consideram as incertezas associadas ao sistema têm sido estudadas. Podem ser destacadas abordagens no domínio da freqüência como a análise µ (Packard et al

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Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters

Boukas

Shi

1998

Int. J. Robust Nonlinear Control

121

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In this paper, we first study the problems of robust quadratic mean‐square stability and stabilization for a class of uncertain discrete‐time linear systems with both Markovian jumping parameters and Frobenius norm‐bounded parametric uncertainities. Necessary and sufficient conditions for the above problems are proposed, which are in terms of positive‐definite solutions of a set of coupled algebraic Riccati inequalities. Then, the problem of robust quadratic guaranteed cost control for the underlying systems is investigated. A guaranteed cost control is designed to ensure the cost function is within a certain bound, irrespective of all admissible uncertainities. © 1998 John Wiley & Sons, Ltd.

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ℋ₂guaranteed cost control for uncertain discrete-time linear systems

Cited by 48 publications

References 7 publications

Gain Scheduled State Feedback Control for Discrete-Time-Varying Polytopic Systems Subject to Input Saturation

Gain Scheduled State Feedback Control for Discrete-Time-Varying Polytopic Systems Subject to Input Saturation

Alocação robusta de pólos através de realimentação de estados dependente de parâmetros

Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters

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ℋ2guaranteed cost control for uncertain discrete-time linear systems

Cited by 48 publications

References 7 publications

Gain Scheduled State Feedback Control for Discrete-Time-Varying Polytopic Systems Subject to Input Saturation

Gain Scheduled State Feedback Control for Discrete-Time-Varying Polytopic Systems Subject to Input Saturation

Alocação robusta de pólos através de realimentação de estados dependente de parâmetros

Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters

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ℋ₂guaranteed cost control for uncertain discrete-time linear systems