First Order Approximation of Partial Stability for Discrete Systems

摘要

The first order approximation of the partial stability of nonlinear time-varying discrete systems is investigated by linearization approach of nonlinear systems. Based on Cauchy matrices solutions and its interceptive Cauchy matrices solutions of homogeneous linear systems, as well as the Gronwall-Bellman inequality, some sufficient conditions of partial stability are obtained for the systems and some of these results are proved to be able to guarantee different exponential convergence rates for partial solutions of the systems.