Improved Approach to Delay-Dependent Stability Analysis of Discrete Time-Delay Systems Interconnected over an Arbitrary Graph

The paper discusses the improvement of the well-posedness, exponential stability and contractiveness whose condition for discrete time-delay systems interconnected over an arbitrary graph. We use the Wirtinger inequality to handle the non-linear terms in the difference equation of the Lyapunov-Krasovskii functional. A sufficient condition for the well-posedness, exponential stability and contractiveness of this kind of discrete time-delay systems is obtained in the form of linear matrix inequalities (LMIs). Taking a numerical example to verify the validity of the obtained results.