On Stability Analysis of Discrete-Time Systems with Constrained Time-Delays via Nonlinear Halanay-Type Inequality

This letter aims to study the problem of stability for discrete-time fully nonlinear time-delay systems with constrained time-varying delays. A delays digraph is used to model the topology of the delay signals. By exploiting the Halanay technique and suitable Lyapunov functions, some sufficient conditions for the global asymptotic stability, uniform global asymptotic stability and global exponential stability are established. A matrix inequality is derived, and it is employed to prove the global exponential stability of linear discrete-time delay systems with delay signals obeying to a delays digraph. Finally, examples are given to illustrate the results.