Robust stability criteria for uncertain discrete-time Lur´e systems with time-varying state-delay and sector-bounded nonlinearity

In this paper, we consider the problem of delay-dependent stability of a class of discrete-time Lur´e systems with time-varying state-delay, and sector-bounded nonlinearity using Lyapunov approach. By exploiting a candidate Lyapunov functional, and using slack matrix variables in the delay-dependent stability analysis, less conservative absolute and robust stability criteria are developed respectively for nominal and uncertain discrete-time Lur´e systems in terms of linear matrix inequalities (LMIs). For deriving robust stability conditions, time-varying norm-bounded uncertainties are considered in the system matrices. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed results.