Robust stability of a class of nonlinear time-varying discrete systems

This paper studies the problem of robust absolute stability of a class of nonlinear discrete-time systems with time-varying matrix uncertainties of polyhedral type and multiple time-varying sector nonlinearities. By using the variational method and the Lyapunov Second Method, criteria for robust absolute stability are obtained in different forms for the given class of systems. Specifically, we determine the parametric class of Lyapunov functions which defines the necessary and sufficient conditions of robust absolute stability. We apply these Lyapunov functions to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations.