Modeling and Qualitative Theory for General Hybrid Dynamical and Control Systems

Abstract

Hybrid dynamical systems which are capable of exhibiting simultaneously several kinds of dynamic behavior, such as continuous-time dynamics, discrete-time dynamics, jump phenomena, switching and logic commands, discrete events, and the like, are of great current interest. In the present paper we employ a general model of dynamical system suitable in the qualitative analysis of such systems. This model of dynamical system allows discontinuous motions, and convergence of motions is relative to generalized time. For the model of hybrid dynamical systems described above, results are established for the principal Lyapunov stability of invariant sets and the principal Lagrange stability of motions. Some of the results of the present paper are applied in the analysis of a specific class of systems.