A new method for global h$$ h $$‐stability analysis for discrete‐time nonlinear systems with time‐varying delays

Abstract

In this paper, we characterize the global ‐stability of discrete‐time nonlinear systems (DTNSs) with time‐varying delays. The global ‐stability encompasses several well‐known types of stability by using different choices of functions, such as global exponential stability (ES), Lagrange exponential stability (LES), and asymptotic stability. By exploiting a direct method based on the system solutions, we give a sufficient condition for the global ‐stability of the DTNSs in the form of simple inequalities that can be easily handled in MATLAB. Finally, numerical examples are presented to demonstrate the applicability of the method.