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

In this paper, a design of a stabilizing state-dependent 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 an algorithm dedicated to solve this class of BMI without loss of generality. The construction of this algorithm is then specified, and the proof of its convergence is given for the two-subsystem 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.