A necessary condition for local asymptotic stability of discrete-time nonlinear systems with parameters

AbstractIn this paper, we derive a necessary condition for local asymptotic stability of equilibria of discrete-time nonlinear systems with parameters. Our necessary condition is analogous to the necessary condition obtained by Byrnes and Sundarapandian [1] for local asymptotic stability of equilibria of continuous-time nonlinear systems with parameters. As a corollary of our general result, we deduce the necessary condition obtained by Lin and Byrnes [2] for local asymptotic stability of equilibria of discrete-time nonlinear systems. We also illustrate our result with some examples