Improved Stability Criteria for Discrete-time Delay Systems via Novel Summation Inequalities

This paper is concerned with the stability analysis of linear discrete time-delay systems. New discrete inequalities for single summation and double summation are presented to estimate summation terms in the forward difference of Lyapunov-Krasovskii functional (LKF), which are more general than some commonly used summation inequalities. Through the construction of an augmented LKF, improved delay-dependent stability criteria for discrete time-delay systems are established. Based on this, a time-delayed controller is derived for linear discrete time-delay systems. Finally, the advantages of the proposed criteria are revealed from the solutions of the numerical examples.