Nontangency-Based Stability Tests for Discrete-Time Dynamical Systems

This paper focuses on stability tests for discrete-time nonlinear dynamical systems with a continuum of equilibria. Two notions that are of particular relevance to such systems are convergence and semistability. In this paper, we develop Lyapunov-based stability tests for decomposable discrete-time nonlinear systems using the notions of nontangency and restricted prolongations. These results do not make any assumptions on the sign definiteness of the Lyapunov function. Several examples are provided to illustrate how our results can be used for analyzing stability and convergence of systems having a continuum of equilibria.