New LMI-based conditions for stability, H&lt;inf&gt;∞&lt;/inf&gt; performance analysis and state-feedback control of rational LPV systems

Bouali, A.; Yagoubi, Mohamed; Chevrel, P.

doi:10.23919/ecc.2007.7068588

Cited by 7 publications

(7 citation statements)

References 20 publications

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“…Yet, we recently noticed that there exists an alternative strategy. It is exploited in [14] and we also found out that it was exploited earlier in [3]. The result also imposes a modification on the Lyapunov certificate Q = V −T P V −1 but does not need the whole machinery of system duality.…”

Section: Introductionmentioning

confidence: 80%

“…As in the seminal papers [13,18] we consider D-stability which corresponds to pole location of linear systems in regions of the complex plane and allows to specify constraints on the times responses of systems such as exponential convergence, damping and frequencies of the oscillating components. As in [11,26,3] we exploit the particularity that Svariable approach is well suited for the study of descriptor systems, which provides convex solutions even for rationaly-dependent uncertain or non-linear systems [16,22,25,7,19].…”

Section: Introductionmentioning

confidence: 99%

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About an Alternative S-Variable Condition for State-Feedback Design

Peaucelle,

Hosoe,

Ebihara

2024

2024 European Control Conference (ECC)

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The study of recent papers brought our attention to an alternative matrix inequality condition for state-feedback design. This condition falls in the category of S-variable results. At the difference of previous conditions it does not involve Schur complement or duality arguments and thus simplifies significantly the mathematical derivations. We provide in this paper a detailed description of the core elements of this new to us result. We then expose some derivations for pole location and time-response performances of uncertain systems with constant or time-varying uncertainties, as well as for some non-linear systems.

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Section: Introductionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

About an Alternative S-Variable Condition for State-Feedback Design

Peaucelle,

Hosoe,

Ebihara

2024

2024 European Control Conference (ECC)

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“…Theorem 1. Let Ω be a polytope of ρ(t) described by (2) and C d (ρ) a linear annihilator of π d described by (14). Given a scalar β, assume there exist symmetric matrices P 0, H i 0, R 0, Q i , and matrices S i , L ∈ R nq×nπ , such that…”

Section: Gs-sof Stabilizationmentioning

confidence: 99%

“…Few works consider a polynomial or rational dependence on the parameter. A paper considering this type of dependence is [14], where a state feedback design was developed for rational LPV systems. In [15], gain-scheduled dynamic output feedback design with H 2 performance has been proposed for rational LPV systems.…”

Section: Introductionmentioning

confidence: 99%

Dissipativity-based $\mathcal{L}_2$ gain-scheduled static output feedback design for rational LPV systems

Viana¹,

Madeira²,

Lima³

2021

Preprint

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This paper proposes the design of gainscheduled static output feedback controllers for the stabilization of continuous-time linear parameter-varying systems with L 2 -gain performance. The system is transformed into the form of a differential-algebraic representation which allows dealing with the broad class of systems whose matrices can present rational or polynomial dependence on the parameter. The proposed approach uses the definition of strict QSR-dissipativity, Finsler's Lemma, and the notion of linear annihilators to formulate conditions expressed in the form of polytopic linear matrix inequalities for determining the gain-scheduled static output feedback control for system stabilization. One of the main advantages of the strategy is that it provides a simple design solution in a non-interactive manner. Furthermore, no restriction on the plant output matrix is imposed. Numerical examples highlight the effectiveness of the proposed method.

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“…In this paper the design of observer-based controllers for rational LPV systems is tackled with via an equivalent descriptor realization with an affine dependency on the varying parameter. This idea was used in (Bouali et al, 2006) and (Bouali et al, 2007a) in the state feedback synthesis case. This paper is organized as fallows.…”

Section: Introductionmentioning

confidence: 99%