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Stability radii of infinite dimensional systems with stochastic uncertainty and their optimization
Author(s) -
Kada M.,
E. Rebiai S.
Publication year - 2006
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1092
Subject(s) - stability (learning theory) , riccati equation , mathematics , radius , lyapunov equation , lyapunov function , state (computer science) , control theory (sociology) , mathematical analysis , computer science , differential equation , control (management) , nonlinear system , physics , algorithm , computer security , quantum mechanics , machine learning , artificial intelligence
Abstract In this paper we consider infinite dimensional systems which are subjected to stochastic structured multiperturbations. We first characterize the stability radii of these systems in terms of a Lyapunov equation and the corresponding Lyapunov inequalities. Then we investigate the problem of maximizing the stability radius by linear state feedback. We show that the supremal achievable stability radius can be determined via the resolution of a parametrized Riccati equation. Illustrative examples are included. Copyright © 2006 John Wiley & Sons, Ltd.