Synthesis of variable gain controllers based on LQ optimal control for a class of uncertain linear systems

This paper proposes a new variable gain controller for a class of uncertain linear systems. The proposed variable gain controller is based on optimal control for the nominal system and consists of the optimal feedback gain and a time-varying adjustable parameter which is designed so as to reduce the effect of uncertainties, i.e. the proposed variable gain controller can achieve good transient performance which is close to LQ optimal control for the nominal system. In this paper, we show sufficient conditions for the existence of the proposed variable gain controller for uncertain linear systems. Finally, numerical examples are presented.