Improved Stability Criteria on Discrete-time Systems with Time-varying and Distributed Delays

In this paper, through constructing some novel Lyapunov-Krasovskii functional (LKF) terms and using some effective techniques, two sufficient conditions are derived to guarantee a class of discrete-time time-delay systems with distributed delay to be asymptotically and robustly stable, in which the linear fractional uncertainties are involved and the information on the time-delays is fully utilized. By employing the improved reciprocal convex technique, some important terms can be reconsidered when estimating the time difference of LKF, and the criteria can be presented in terms of linear matrix inequalities (LMIs). Especially, these derived conditions heavily depend on the information of time-delay of addressed systems. Finally, three numerical examples demonstrate that our methods can reduce the conservatism more efficiently than some existing ones.