A Design Method of Variable Gain Robust Controllers with Guaranteed Gain Performance for a Class of Uncertain Switched Linear Systems
Hidetoshi Oya *
The Institute of Technology and Science, The University of Tokushima, 2-1 Minamijosanjima, Tokushima, Japan.
Kojiro Hagino
The Graduate School of Informatics and Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo, 182-8585, Japan.
*Author to whom correspondence should be addressed.
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.
Keywords: switched linear systems, guaranteed L2 gain performance, variable gain controllers,, compensation inputs