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Journal Articles Nonlinear Analysis: Hybrid Systems Year : 2011

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

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.

Dates and versions

hal-00625666 , version 1 (22-09-2011)

Identifiers

Cite

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, 2011, 5 (4), pp.647-654. ⟨10.1016/j.nahs.2011.05.002⟩. ⟨hal-00625666⟩
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