A Design Method of Variable Gain Robust Controllers with Guaranteed Gain Performance for a Class of Uncertain Switched Linear Systems

Abstract

This paper discusses a design problem of a variable gain robust controller with guaranteed  gain performance for a class of uncertain switched linear systems. The uncertainties included in the switched linear system under consideration are supposed to satisfy the matching condition and the proposed variable gain robust controller consists of a switching rule, state feedback laws with fixed and variable feedback gain matrices. The switching rule and the fixed feedback gain matrices are derived by using the nominal system. In this paper, we show that a design method of the variable gain robust controller with guaranteed  gain performance are reduced to matrix inequalities. Besides, it is presented that the number of matrix inequalities in the proposed design is less than one for the existing results. Finally, an illustrative example is included.