Lyapunov Matrices Approach to Robust Stability Analysis for Linear Discrete-Time Systems with Multiple Delays

This paper investigates the problem of the robust stability analysis of linear uncertain discrete-time systems with multiple delays. For this end, we first introduce the concept of Lyapunov matrix which based on the fundamental matrix of the corresponding nominal systems. At the same time, the existence and uniqueness of Lyapunov matrix can be promised when the nominal system is exponentially stable. Furthermore, by constructing Lyapunov matrix-based Lyapunov-Krasovskii functional, the sufficient condition of robust exponential stability for the considered systems is proposed. Finally, a numerical example illustrates the validity of the obtained results.