The solution concept
The solution concept
This chapter details a rigorous development of the concept of a solution to a hybrid system. The data of a hybrid system is defined with an introduction of some basic terminology regarding set-valued mappings, and a generalized concept of time is then introduced. The chapter also defines the solutions to a hybrid system and it addresses the basic properties of solutions, like their existence and uniqueness. The concept of a solution is further illustrated by hybrid models of switching systems under broad families of switching signals. Broadly speaking, switching systems are continuous-time systems given by a family of differential equations, where the particular differential equation that governs the evolution of the state at a given time instant is determined by a switching rule/signal.
Keywords: uniform asymptotic stabilitys, closeds sets, equilibriums pointss, pre-asymptotic stabilitys, Lyapunovs functions, Lyapunovs conditions, dynamical systemss
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