Journal of Applied & Computational Mathematics

Exponential Stability of Nonlinear Nonautonomous Multivariable Discrete Systems

Abstract

Gil M

We consider a class of nonautonomous discrete-time systems governed by semilinear vector difference equations with slowly varying linear parts. Sharp exponential stability conditions are suggested. They are formulated in terms of the eigenvalues of the coefficients and constants characterizing the nonlinearities. Our approach is based on the recent norm estimates for solutions of matrix equations.