Converging algorithm for a class of BMI applied on state dependant stabilization of switched systems

Alexandre Kruszewski 1 Romain Bourdais 2 Wilfrid Perruquetti 3, 1
1 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
3 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : In this paper, a design of a stabilizing state dependant switching law is presented. First, it is based on a new reformulation of this control problem into a class of BMI (Bilinear Matrix Inequality) problem. The originality of this reformulation is that it will be used, in a second part, by a an algorithm dedicated to solve this class of BMI without loss of generality. The construction of this algorithm is then speci¯ed, and the proof of its convergence is given for the two subsystems case. The last part of the work consists in presenting the problem for a polytopic switching system, and how the previous algorithm can be extended. The proposed scheme is illustrated by an academical example.
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Submitted on : Thursday, September 22, 2011 - 11:23:20 AM
Last modification on : Tuesday, April 2, 2019 - 2:17:12 AM

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Alexandre Kruszewski, Romain Bourdais, Wilfrid Perruquetti. Converging algorithm for a class of BMI applied on state dependant stabilization of switched systems. Nonlinear Analysis: Hybrid Systems, Elsevier, 2011, 5 (4), pp.647-654. 〈10.1016/j.nahs.2011.05.002〉. 〈hal-00625666〉

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