Robust H2 performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs

Abstract : A particular class of uncertain linear discrete-time periodic systems is considered. The problem of robust stabilization of real polytopic linear discrete-time periodic systems via a periodic state-feedback control law is tackled here, along with H2 performance optimization. Using additional slack variables and the periodic Lyapunov lemma, an extended sufficient condition of robust H2 stabilization is proposed. Based on periodic parameter-dependent Lyapunov functions, this last condition is shown to be always less conservative than the more classic one based on the quadratic stability framework. This is illustrated on a numerical example from the literature.
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https://hal.archives-ouvertes.fr/hal-00168061
Contributor : Jamal Daafouz <>
Submitted on : Friday, August 24, 2007 - 11:29:08 AM
Last modification on : Friday, April 12, 2019 - 4:22:18 PM

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Christophe Farges, Dimitri Peaucelle, Denis Arzelier, Jamal Daafouz. Robust H2 performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs. Systems and Control Letters, Elsevier, 2007, 56 (2), pp.159-166. ⟨10.1016/j.sysconle.2006.08.006⟩. ⟨hal-00168061⟩

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