Robust absolute stability of time-varying nonlinear discrete-time 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 class of systems under consideration. Specifically, we determine the parametric classes of Lyapunov functions which define the necessary and sufficient conditions of robust absolute stability. We apply the piecewise-linear Lyapunov functions of the infinity vector norm type to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations. Some simple sufficient conditions of robust absolute stability are given which become necessary and sufficient for several special cases. An example is presented as an application of these results to a specific class of systems with time-varying interval matrices in the linear part.