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