H∞ control for multirate sampled-data system with time-delay

In this paper, we study H_∞ control for multirate sampled-data system with time-delay. In allusion to the problems of time-delay and multirate sampling, we describe the system with a time-varying jump system characterization. Then basing on the technique of continuous lifting, the hybrid, linear, time-varying, jump system is isometrically mapped to a discrete-time, linear, time-varying system with infinite-dimensional input-output spaces. Finally by making use of the definition of the system function for a discrete-time, time-varying system and the property of symplectic pair, the infinite-dimensional system is transformed to an equivalent discrete-time system with finite-dimensional input-output spaces which can be disposed with well developed H_∞ control theory. As a result, the proposed design method can solve H_∞ control problem for multirate sampled-data system with time-delay.