Delay Dependent Stability Criteria a Stabilization for Discrete-Time Syste Via Three Terms approximation

Abstract

This paper discusses the problem of delay-dependent stability and stabilization for discrete-time linear systems. By employing a three-term approximation for delayed state variables, a new model transformation is developed, which has a smaller approximation error than the two-term approach. New delay-dependent stability conditions are proposed and formulated as linear matrix inequalities (LMIs), by using scaled small gain theorem and a simpleLyapunov-Krasovskii functional. Before the end, a state feedback controller has investigated in the stabilization of discrete linear systems. Finally, numerical examples are presented to illustrate the effectiveness of the proposed method.