A comparison theory for stability analysis of discontinuous dynamical systems. I. Results involving stability preserving mappings

摘要

In the present paper, we develop a general comparison theory for Lyapunov and Lagrange stability analysis of discontinuous dynamical systems, making use of stability preserving mappings. To demonstrate the applicability of our results, we consider specific classes of nonlinear discontinuous dynamical systems. Further, in a companion paper we specialize the present results by employing vector Lyaponov functions.