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Hybrid Dynamical SystemsModeling, Stability, and Robustness$
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Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel

Print publication date: 2012

Print ISBN-13: 9780691153896

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691153896.001.0001

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The solution concept

The solution concept

Chapter:
(p.25) Chapter Two The solution concept
Source:
Hybrid Dynamical Systems
Author(s):

Rafal Goebel

Ricardo G. Sanfelice

Andrew R. Teel

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691153896.003.0002

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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