In this paper some convex conditions are presented in the form of linear matrix inequalities (LMIs), yielding sufcient conditions for testing the robust stability of uncertain discrete-time systems with time-varying delay. In the sequel, LMI conditions for design robust state feedback gains are obtained. Two types of delay conditions are proposed: delay dependent and delay independent. Both of them are convex and employ extra matrices to achieve less conservative results. Examples from the literature are used to compare the performance of the conditions proposed here with the results obtained in other papers. It is presented a study of a model with polyopic uncertainty obtained from an industrial electric heater. In this study, the uncertain system is stabilized by means of the LMI conditions proposed here.
Uncertain discrete-time systems; Time varying delay; Lyapunov-Krasovskii functionals; Linear matrix inequalities
