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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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Perturbations and generalized solutions

Perturbations and generalized solutions

Chapter:
(p.73) Chapter Four Perturbations and generalized solutions
Source:
Hybrid Dynamical Systems
Author(s):

Rafal Goebel

Ricardo G. Sanfelice

Andrew R. Teel

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691153896.003.0004

This chapter discusses the effect of state perturbations on solutions to a hybrid system. It shows that state perturbations, of arbitrarily small size, can dramatically change the behavior of solutions. While such a phenomenon is also present in continuous-time and discrete-time dynamical systems, it is magnified in the hybrid setting, due to the flows and the jumps being constrained to the flow and the jump sets, respectively. Perturbations affecting the whole state of a hybrid system are usually considered. The resulting behaviors are quite representative of what may occur if perturbations come from state measurement error in a hybrid feedback control system or from errors present in numerical simulations of hybrid systems. The case of hybrid feedback control is given some attention in this chapter. Also, throughout the chapter, effects of perturbations are related to the regularity properties of the data of hybrid systems.

Keywords:   state perturbations, generalized solutions, Krasovskii solutions, Hermes solutions, hybrid feedback control, regularity properties, state measurement error, numerical simulations

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