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A Convex Approach to Robust Stability for Linear Systems with Uncertain Scalar Parameters

Abstract : In this report, robust stability for linear systems with several uncertain (complex and/or real) scalar parameters, is studied. Necessary and sufficient conditions for robust stability are given, in terms of solvability of some simple linear matrix inequalities (LMIs). This result constitutes an extension of the characterization by solvability of Lyapunov inequality, of the asymptotic stability for usual linear systems. The related issue of delay-independent stability for linear systems with multiple (noncommensura- te) delays is also treated, and it is shown how the approach used here is linked to the search for quadratic Lyapunov-Krasovskii functional of a special type.
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https://hal.inria.fr/inria-00072271
Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 8:16:23 PM
Last modification on : Friday, May 25, 2018 - 12:02:04 PM
Long-term archiving on: : Sunday, April 4, 2010 - 11:01:30 PM

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  • HAL Id : inria-00072271, version 1

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Pierre-Alexandre Bliman. A Convex Approach to Robust Stability for Linear Systems with Uncertain Scalar Parameters. [Research Report] RR-4316, INRIA. 2001. ⟨inria-00072271⟩

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