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A Novel Approach to Delay-Variation-Dependent Stability Analysis of 2-D Discrete-Time Systems With Mixed Delays

In this paper, a stability analysis problem is studied for a class of two-dimensional (2-D) discrete-time systems with time-varying and distributed delays described by the second Fornasini-Marchesini (FM) model. First, new 2-D polynomials-based summation inequalities are proposed to estimate summation terms in the forward difference of Lyapunov-Krasovskii functional (LKF). The inequalities can reduce to 2-D Jensen inequalities and 2-D finite-sum inequalities by designing slack matrices and arbitrary vectors. Second, a new augment LKF is constructed, which makes full use of the delay changing information. By the Lyapunov stability theory, sufficient conditions for asymptotic stability of 2-D discrete-time systems are derived in the form of linear matrix inequalities. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed methods.