Robust mixed H 2 /H ∞ control of time-varying delay systems

This paper describes the mixed H 2 /H X controller design method of linear systems with time-varying delays in both state and control input. More specifically, the proposed mixed H 2 /H X controller minimizes the H 2 performance measure when satisfying a prescribed H X norm bound on the closed loop system. The sufficient conditions for the existence of controller, the mixed H 2 /H X controller design method and the upper bound of performance measure are presented using the linear matrix inequality (LMI) technique. Also, all solutions including controller gain and the upper bound of performance measure are obtained simultaneously. Furthermore, the proposed controller design method can be easily extended into the problem of robust mixed H 2 /H X controller design method for parameter uncertain systems with time-varying delays in both state and control input.