A Local Nonlinear Small-Gain Theorem for Discrete-Time Feedback Systems and Its Applications

摘要

In this work we discuss nonlinear small-gain theorems in the framework of input-to-state stability for discrete time systems. Our primary objective is to show that, as in the continuous-time context, these discrete-time nonlinear small-gain theorems are very effective in stability analysis and synthesis for various classes of discrete-time control systems. A converse Lyapunov theorem for discrete exponential stability is developed to assist these applications. New results in stability and stabilization presented in this paper are significant extensions of previous work by other authors [13, 18].