Convex analysis and synthesis for uncertain discrete-time systems with time-varying state delay

The class of polytopic uncertain discrete-time systems with time-varying delays is investigated in this paper. Firstly, some convex conditions are presented in the form of linear matrix inequalities (LMIs) to test robust stability. Then, LMI conditions to design robust state feedback gains are proposed. Both, delay-dependent and delay-independent conditions are formulated as convex feasibility problems employing extra matrices that yield less conservative results. Some numerical examples are presented to illustrate the application of the conditions for analysis and synthesis of robust state feedback gains.