The purpose of this paper is to establish discrete versions of the well-known Lyapunov’s stability theorem and LaSalle’s invariance theorem for a non-autonomous discrete dynamical system. Our proofs for these theorems are constructive in the sense that they are made by explicitly building a Lyapunov function for the system. A comparison between non-autonomous discrete dynamical systems and cont...

A complete Lyapunov function characterizes the behaviour of a general discrete-time dynamical system. In particular, it divides state space into chain-recurrent set where is constant along trajectories and part flow gradient-like strictly decreasing solutions. Moreover, level sets provide information about attractors, repellers, basins attraction. style='text-indent...

As a method to establish the Lyapunov stability of differential/difference equations systems, the LaSalle invariance principle was originally proposed in the 1950’s and has become a fundamental mathematical tool in the area of dynamical systems and control. In both theoretical research and engineering practice, discrete-time dynamical systems have been at least as extensively studied as continu...