Finite-dimensional dynamical systems

Abstract

We present the principal stability and boundedness results for continuous dynamical systems, discrete-time dynamical systems, and discontinuous dynamical systems involving monotonic and non-monotonic Lyapunov functions. We apply the results of Chapter 3 to arrive at these results. When considering various stability types, our focus is on invariant sets that are equilibria. Our results constitute sufficient conditions (the Principal Stability and Boundedness Results) and necessary conditions (Converse Theorems). We demonstrate the applicability of all results by means of numerous examples. We also present results for uniform stability and for uniform asymptotic stability in the large involving multiple non-monotonic Lyapunov functions. The applicability of these results is demonstrated by means of a specific example.