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# Nonconservative LMI Criteria for Characterization of Delay-Independent Properties of Delay Systems. Application to Stability and Input-Output Analysis of Systems with Complex Parameter

Abstract : This report focuses on delay-independent stability and delay-independent input-output properties (passivity, $H_\infty$ performance, circle criterion, Popov criterion) of delay systems. The main results show that, as it is the case for the usual, rational, systems, the properties under study here may be characterized by solvability of some linear matrix inequalities. The latter are constructed by use of some quadratic Lyapunov-Krasovskii functionals, generalizing a well-known class. The method also applies to the analysis of systems with uncertain complex parameter, for which the results are related to the search for analytic parameter-dependent Lyapunov functions. Illustrative examples are provided.
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https://hal.inria.fr/inria-00072309
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Submitted on : Tuesday, May 23, 2006 - 8:22:09 PM
Last modification on : Thursday, February 3, 2022 - 11:14:36 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:07:55 PM

### Identifiers

• HAL Id : inria-00072309, version 1

### Citation

Pierre-Alexandre Bliman. Nonconservative LMI Criteria for Characterization of Delay-Independent Properties of Delay Systems. Application to Stability and Input-Output Analysis of Systems with Complex Parameter. [Research Report] RR-4278, INRIA. 2001. ⟨inria-00072309⟩

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