H Infinite Stabilization of Uncertain Piecewise Linear Systems with Filippov Solutions

Abstract

This paper is concerned with robust stabilization and H infinite control of piecewise linear switched systems subject to uncertainty in the context of Filippov solutions. The analysis developed here encapsulates solutions with infinite switching in finite time. First, a set of linear matrix inequalities are brought forward which determines suficient conditions to investigate the asymptotic stability of Filippov solutions. Then, a method to construct robust stabilizing switching controllers is proposed. Subsequently, the latter result is extended to switching controllers with H infinite performance. The suggested controller synthesis schemes are based on solving sets of bilinear matrix inequalities for which appropriate algorithms are delineated.