Delay-variation-dependent summation inequality and its application to stability analysis of discrete-time systems with time-varying delay

This work tends to research the stability of the discrete -time systems with a time -varying delay based the Lyapunov-Krasovskii functional (LKF) method. In order to acquire a less conservative stability criterion, some techniques in this work are refined and taken into use. Firstly, to reduce the conservatism generated when estimating the forward difference of the LKF, a newly delay -variation -dependent summation inequality constructed, which includes the existing free -matrix -based and Bessel function -based summation inequalities, using delay -variation -product relaxed matrices to provide more freedom for the estimation results. Secondly, further show the influence of the introduced variation information in the time -varying delay, we give another selection of the allowable delay set for the delayed discrete -time systems. Thirdly, by taking advantages the above method and by constructing a delay -product -type LKF, using extended free -weighting -matrices zero equations, and considering different allowable delay sets, two improved linear matrix inequality (LMI)-based delay -variation -dependent criteria for delayed discrete -time systems are formulated. Some classical numerical instances are presented to explain the effectiveness of these proposed stability criteria.