DYNAMICAL SYSTEMS - PART I : RESULTS INVOLVING

In the present paper, we develop a general cornparison theory for Lyapunov and Lagrange stability analysis of discontinuous dynamical systems, making use of sta- bility preserving mappings. To demonstrate the appli- cability 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.