A new variable gain controller for a class of uncertain linear systems via piecewise Lyapunov functions — Less conservative LMI conditions —

In this paper, we present a new variable gain controller for a class of uncertain linear systems via piecewise Lyapunov functions. The proposed variable gain controller is designed so as to reduce the effect of uncertainties and achieves good transient performance which is close to desired trajectory. In this paper, on the basis of the concept of piecewise Lyapunov functions, we show new LMI conditions for the existence of the proposed variable gain controller for uncertain linear systems. The proposed LMI conditions are useful, because the LMI conditions are less conservative comparing with the existing results. Finally, numerical examples are presented.