Robust stabilisation for a class of discrete-time systems with time-varying delays via delta operators

The problem of robust state feedback control using delta operator approach for a class of linear fractional uncertain systems with time-varying delays is investigated. Based on Lyapunov–Krasovskii functional in delta domain, a new delay-dependent state feedback controller is presented in terms of linear matrix inequalities. The sampling-period T is an explicit parameter, and thus it is easy to observe and analyse the effect of the state feedback controller with different sampling periods. The proposed method can unify some previous related continuous and discrete systems into the framework of delta operator systems. Numerical examples are given to illustrate the effectiveness of the developed techniques.