A New Model Transformation of Discrete-Time Systems With Time-Varying Delay and Its Application to Stability Analysis

This technical note focuses on analyzing a new model transformation of uncertain linear discrete-time systems with time-varying delay and applying it to robust stability analysis. The uncertainty is assumed to be norm-bounded and the delay intervally time-varying. A new comparison model is proposed by employing a new approximation for delayed state, and then lifting method and simple Lyapunov-Krasovskii functional method are used to analyze the scaled small gain of this comparison model. This new approximation results in a much smaller error than the existing ones. Based on the scaled small gain theorem, new stability criteria are proposed in terms of linear matrix inequalities. Moreover, it is shown that the obtained conditions can be established through direct Lyapunov method. Two numerical examples are presented to illustrate the effectiveness and superiority of our results over the existing ones.