Robust stability and H∞ control of uncertain piecewise linear switched systems with Filippov solutions

This paper addresses the robust stability and control problem of uncertain piecewise linear switched systems where, instead of the conventional Carathéodory solutions, we allow for Filippov solutions. In other words, in contrast to the previous studies, solutions with infinite switching in finite time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, based on earlier results, the stability problem of piecewise linear systems with Filippov solutions is translated into a number of linear matrix inequality feasibility tests. Subsequently, a set of matrix inequalities are brought forward, which determines the asymptotic stability of the Filippov solutions of a given uncertain piecewise linear system. Afterwards, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed H_∞ performance are formulated. Finally, a V-K iteration algorithm is proposed to surmount the aforementioned matrix inequality conditions.