An Extension of Popov Criterion to Multivariable Time-Varying Nonlinear Systems. Application to Criterion for Existence of Stable Limit Cycles - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 1998

An Extension of Popov Criterion to Multivariable Time-Varying Nonlinear Systems. Application to Criterion for Existence of Stable Limit Cycles

Abstract

This report deals with sufficient conditions for absolute stability of multivariable control systems. The proposed conditions extend in a simple way the classical Popov criterion to time-varying memoryless nonlinearities. They are expressed in terms of some Linear Matrix Inequalities (LMIs). A weaker frequency domain criterion is deduced, leading to a simple graphical interpretation. The results ensure in general local stability, however, the stability is global for example for linear time-varying systems. As an application, a Popov-like criterion for existence of stable periodic solutions for periodic systems is proposed, using previous results by the authors.
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Dates and versions

inria-00073172 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00073172 , version 1

Cite

Pierre-Alexandre Bliman, Alexander M. Krasnosel'Skii. An Extension of Popov Criterion to Multivariable Time-Varying Nonlinear Systems. Application to Criterion for Existence of Stable Limit Cycles. [Research Report] RR-3512, INRIA. 1998. ⟨inria-00073172⟩
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