Sliding mode design via quadratic performance optimization with pole-clustering constraint

Abstract

We consider a novel method for designing the sliding mode that minimizes the quadratic performance while keeping a pole-clustering constraint. Our approach is based on the manipulations of linear matrix inequalities (LMIs) imposed by the design objectives. For this purpose, we newly propose LMI conditions for the quadratic performance optimization and the pole-clustering problem, respectively, in a full order state. Then they are combined in the LMI framework that is typically devised for the sliding mode design in the convex form. An effort is made to reduce the generic conservatism by allowing different Lyapunov matrices. In addition, a class of polytope uncertain systems is addressed to illustrate the advantages of the proposed method.