Robust H∞ Control for Class of Discrete-Time Markovian Jump Systems with Time-Varying Delays Based on Delta Operator

In this paper, the problem of robust H∞ state feedback control using a delta operator approach for a class of linear fractional uncertain jump systems with time-varying delays is investigated. Based on the Lyapunov–Krasovskii functional in the delta domain, a new delay-dependent H∞ state feedback controller which requires both robust stability and a prescribed H∞ performance is presented in terms of linear matrix inequalities. The sampling period T appears as an explicit parameter; therefore, it is easy to observe and analyze the effect of the results with different sampling periods. Furthermore, the proposed method can unify some previous related continuous and discrete systems into the framework of delta operator systems. Numerical examples are presented to illustrate the effectiveness of the developed techniques.