LQ Optimal Control-Based Variable Gain Controllers for Linear Systems with Structured Uncertainties and Its Performance Analysis

This paper proposes a variable gain controller for a linear system with structured uncertainties. The proposed variable gain controller is based on LQ 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. The proposed LQ optimal control-based variable gain controller can achieve good transient performance which is close to LQ optimal control for the nominal system and adjust the magnitude of the control input. In this paper, we show sufficient conditions for the existence of the proposed variable gain robust controller for the uncertain linear system. Finally, an illustrative example is included.