New results on quadratic stabilization of switched linear systems with polytopic uncertainties

In this paper, the quadratic stabilization of switched linear systems with polytopic uncertainties is considered. Compared with the existing result, a more general switching control method is proposed to guarantee the quadratic stabilization. This switching control method is based on the partition of vertex matrix set of each subsystem. By this method, the matrix inequalities needed to be solved are always less than that needed to be solved before except one extreme case, for this case, it is equal. The switched control synthesis problem is also studied for both switched state feedback and output feedback. Several bilinear matrix inequalities (BMIs) based conditions are derived for both cases, respectively.