Robust stability conditions for systems with distributed delays

Santos, Omar; Mondié, Sabine; Kharitonov, Vladimir L.

doi:10.1109/cdc.2006.376832

Cited by 21 publications

(6 citation statements)

References 8 publications

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“…To conclude, if the LMI conditions (17) and (18) are satisfied, the functional meets the requirements of the Lyapunov-Krasovskii theorem, (19) and 23…”

Section: Theorem 4 Consider Systemmentioning

confidence: 97%

“…In order to avoid this strong constraint, another possibility, described by Gu et al [8], is to use a very general class of Lyapunov Krasovskii functional (see for instance [18]) and a discretization scheme to obtain numerically tractable stability conditions. This technique designed for piecewise constant delay kernel leads to a reduction of conservatism at the expense of the numerical burden.…”

Section: Introductionmentioning

confidence: 99%

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Complete quadratic Lyapunov functionals for distributed delay systems

2015

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International audienceThis paper is concerned with the stability analysis of distributed delay systems using complete-Lyapunov functionals. Numerous articles aim at approximating their parameters thanks to a discretization method or polynomial modeling. The interest of such approximations is the design of tractable sufficient stability conditions. In the present article, we provide an alternative method based on polynomial approximation which takes advantages of the Legendre polynomials and their properties. The resulting stability conditions are scalable with respect to the maximum degree of the polynomials and are expressed in terms of tractable linear matrix inequalities. Several examples of delayed systems are tested to show the effectiveness of the method

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“…To conclude, if the LMI conditions (17) and (18) are satisfied, the functional meets the requirements of the Lyapunov-Krasovskii theorem, (19) and 23…”

Section: Theorem 4 Consider Systemmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Complete quadratic Lyapunov functionals for distributed delay systems

2015

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“…Assume system (1) to be asymptotically stable. If the disturbances in system (2) satisfy condition (8), then the perturbed system (2) is asymptotically stable.…”

Section: Lemma 2 Let System (1) Satisfy the Lyapunov Condition Ifmentioning

confidence: 99%

Robust stability analysis for linear systems with distributed delays: A time‐domain approach

Juárez

Аlexandrova

Mondié

2020

Intl J Robust & Nonlinear

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This work is devoted to the robust stability analysis of linear systems with distributed delays. The approach is based on recent results in the Lyapunov-Krasovskii framework, where a Lyapunov-Krasovskii functional with prescribed negative definite derivative is applied. The stability conditions obtained in this work, are simple inequalities which depend on the so-called delay Lyapunov matrix. The cases of matrix parameters and delays uncertainties are addressed, accurately detecting exact stability bounds when applied in an iterative manner. Our method is used successfully to tackle the challenging problem of robust predictor-based stabilization of systems with state and input delays.

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“…The complete-type functionals were shown to be effective in solving the problems we address in this paper: for systems with concentrated delays, they were applied to obtention of the robustness bounds (see [7]) and to construction of the exponential estimates (see [8]). The results were generalized to the distributed delay case in [12] and [13]. The main point, allowing the functionals to be useful, is that they admit the quadratic lower bounds, see [12] for the distributed delay case.…”

Section: Introductionmentioning

confidence: 99%

Exponential estimates for solutions of linear systems with distributed delay

Medvedeva

2015

2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP)

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Abstract-In this paper, for a class of linear time-invariant systems with distributed delay, the robust stability conditions are obtained, and the exponential estimates for the solutions are constructed. The results are derived within the framework of the Lyapunov-Krasovskii functionals with a given derivative. The functional, that does not admit a quadratic lower bound and therefore is considered to be inappropriate for the robustness analysis, is used.

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Robust stability conditions for systems with distributed delays

Cited by 21 publications

References 8 publications

Complete quadratic Lyapunov functionals for distributed delay systems

Complete quadratic Lyapunov functionals for distributed delay systems

Robust stability analysis for linear systems with distributed delays: A time‐domain approach

Exponential estimates for solutions of linear systems with distributed delay

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