Robust Stability of Lurie Nonlinear Discrete System with Time-Varying Delay via Scaled Small Gain Theorem

This paper is concerned with the robust stability of lurie nonlinear discrete time-varying delay system. The initial lurie nonlinear discrete system with time-varying delay is converted into two interconnected subsystems by using a model transformation. One of the subsystems has no uncertainty and delay and can be analyzed stability by Lyapunov-Krasovskii functional method. Then using an input-output (IO) approach which is an application of the scaled small gain theorem to obtain the stability condition of the lurie nonlinear discrete system. A numerical example is provided to demonstrate the applicability of the presented method.