Robust exponential H∞H∞ control for uncertain time-varying delay systems with input saturation: A Markov jump model approach

This paper is concerned with the state feedback stabilization problem for uncertain time-varying delay systems with input saturation. Based on the stochastic property of time-varying delay, the considered system can be transformed into a continuous Markov jump system with stochastic delays, where the growth trend and the maximum value of the time-varying delay are limited. The problem we address is to design a robust state feedback controller which can switch with time-varying delay in terms of Markov process, such that the system is exponentially mean-square stable with disturbance attenuation γγ. Conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities (LMIs). When these LMIs are feasible, the desired robust controller is given. Finally, two examples are provided to demonstrate the effectiveness of the proposed approach.