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 on 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 is 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, to 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 of 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.