LMI characterization of structural and robust stability

Geromel, J.C.; Oliveira, Maurı́cio C. de; Hsu, Liu

doi:10.1016/s0024-3795(98)10123-4

Cited by 172 publications

(130 citation statements)

References 6 publications

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“…The LMIs here are very similar to those known from the literature (see, for example, [2,9,15]) for 1D linear systems. This does not, of course, mean that repetitive processes can be analyzed by direct application of existing 1D linear systems theory, merely that in some cases recourse can be made to tools from this latter area.…”

Section: Remarksupporting

confidence: 64%

“…In effect, this control law is composed of a weighted sum of current pass state feedback and feedforward of the previous pass profile. The LMI of (9.5) extends in a natural manner to the design of (9.10) for stability along the pass but here we will use the approach based on [2,9,15] and first adopted for repetitive processes in [6]. This will prove to be of particular use in the analysis of the case when there is uncertainty associated with the process state-space model.…”

Section: Stability and Stabilization Of Discrete Linear Repetitive Prmentioning

confidence: 99%

“…Hence, although the nominal process is most often time invariant, the uncertain process can be time-varying. This will be the case here and to solve the problem we generalize previously reported LMI based design algorithms for uncertain discrete linear repetitive processes [5] and other classes of systems [2,9,15] with polytopic uncertainty. These results are based on sufficient, but not necessary, stability conditions.…”

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confidence: 99%

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Robust Control of Discrete Linear Repetitive Processes with Parameter Varying Uncertainty

Cichy

Gałkowski

Rogers

et al. 2011

Lecture Notes in Electrical Engineering

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Repetitive processes propagate information in two independent directions where the duration of one of these is infinite.They pose control problems that cannot be solved by application of results for other classes of 2D systems. This paper develops robust controller design algorithms for discrete linear processes based on the poly-quadratic stability that produce less conservative results than currently available alternatives. IntroductionRepetitive processes are a distinct class of 2D systems of both system theoretic and applications interest whose unique characteristic is a series of sweeps, termed passes, through a set of dynamics defined over a fixed finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a

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Section: Remarksupporting

confidence: 64%

Section: Stability and Stabilization Of Discrete Linear Repetitive Prmentioning

confidence: 99%

mentioning

confidence: 99%

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Robust Control of Discrete Linear Repetitive Processes with Parameter Varying Uncertainty

Cichy

Gałkowski

Rogers

et al. 2011

Lecture Notes in Electrical Engineering

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“…Considerando apenas sistemas lineares incertos contínuos e invariantes no tempo, dentre os testes de estabilidade robusta baseados em funções de Lyapunov dependentes de parâmetros destacam-se, por estarem formulados em termos de LMIs e pela facilidade de resolução numérica, as abordagens apresentadas em (Geromel, de Oliveira e Hsu, 1998) e (Peaucelle et al, 2000). Em (Geromel, de Oliveira e Hsu, 1998), condições suficientes para a estabilidade estrutural de uma classe de sistemas foram propostas em termos de LMIs, sendo estabelecidas as conexões desses resultados com positividade real e passividade em sistemas lineares.…”

Section: Introductionunclassified

“…Em (Geromel, de Oliveira e Hsu, 1998), condições suficientes para a estabilidade estrutural de uma classe de sistemas foram propostas em termos de LMIs, sendo estabelecidas as conexões desses resultados com positividade real e passividade em sistemas lineares. Uma extensão desses resultados é apresentada em (Peaucelle et al, 2000), tratando diferentes regiões convexas dentro do plano complexo.…”

Section: Introductionunclassified

Estabilidade robusta de sistemas lineares através de desigualdades matriciais lineares

Leite

Montagner

Oliveira

et al. 2004

Sba Controle & Automação

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Sufficient conditions for the analysis of stability of linear systems with polytopic uncertainties are presented in this paper. The robust stability is guaranteed by the existence of a parameter dependent Lypaunov function obtained from the feasibility test of a set of linear matrix inequalities (LMIs) formulated at the vertices of the uncertainty polytope. Three conditions are presented, and the results are also compared with the analysis based on quadratic stability (same Lyapunov function for the entire set of uncertainties), for continuous as well as discrete-time systems. The first condition exploits the use of some extra variables (matrices) in the LMIs, and the second one uses a larger number of LMIs. These two conditions have recently appeared in the literature and are less conservative than quadratic stability. The third condition, proposed in this paper, combines the two ideas, yielding better results, and contains the previous conditions as particular cases. Several examples are presented to illustrate the Artigo submetido em 13/03/03 1a. Revisão em 20/10/03 Aceito sob recomendação do Ed. Assoc. Prof. Liu Hsu numerical performance of the LMI conditions in terms of efficiency and computational complexity.

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Coprime factorization of polytopic LPV systems based on a homogeneous polynomial approach

Pereira

Kienitz

Oliveira

2020

Asian Journal of Control

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This paper presents novel linear matrix inequalities (LMI)-based conditions to address the coprime factorization problem for polytopic linear parametervarying (LPV) systems in both the continuous-and discrete-time cases. The proposed conditions rely on the use of homogeneous polynomial parameterdependent (HPPD) matrix solutions of arbitrary degree g, which are used to obtain coprime factorization descriptions subject to time-varying parameters defined inside a polytopic structure with known vertices. For a given degree g, synthesis of right and left coprime factorizations in terms of two special state-feedback and filtering problems under quadratic H 2 performance are provided. Existence conditions are given from linear matrix inequalities relaxations based on an extension of Pólya's theorem and the HPPD approach. The effectiveness of the proposed conditions is evaluated by means of numerical examples.

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LMI characterization of structural and robust stability

Cited by 172 publications

References 6 publications

Robust Control of Discrete Linear Repetitive Processes with Parameter Varying Uncertainty

Robust Control of Discrete Linear Repetitive Processes with Parameter Varying Uncertainty

Estabilidade robusta de sistemas lineares através de desigualdades matriciais lineares

Coprime factorization of polytopic LPV systems based on a homogeneous polynomial approach

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