ABSTRACT
The present chapter consists of five parts. In the first section we establish a general framework for the qual-
itative analysis of hybrid dynamical systems by introducing a notion of generalized time and by using this concept to establish a definition of general hybrid dynamical system. This model includes most of the important classes of hybrid dynamical systems considered in the current literature. Next, in the second section we consider several specific classes of hybrid dynamical systems (defined on generalized time). Similarly as in Chapter 3 (see Sections 3.1 and 3.2), we provide the qualitative characterizations of invariant sets and of motions for hybrid dynamical systems (defined on generalized time) in the third section of the chapter. In the fourth section we show that hybrid dynamical systems defined on generalized time (as defined in
the first section), can always be embedded into dynamical systems defined on real time, having identical qualitative properties, with the consequence that the qualitative study of general hybrid dynamical systems defined on generalized time can be reduced to the study of dynamical systems defined on real time; the latter, however, may have motions that are not continuous or not smooth with respect to time.
