Stability of hybrid systems: state of the art

This paper collects work on the stability analysis of hybrid systems. The hybrid systems considered are those that combine continuous dynamics (represented by differential or difference equations) with finite dynamics, usually thought of as being a finite automaton. We review multiple Lyapunov funct...

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Bibliographic Details
Published inProceedings of the 36th IEEE Conference on Decision and Control Vol. 1; pp. 120 - 125 vol.1
Main Author Branicky, M.S.
Format Conference Proceeding
LanguageEnglish
Published IEEE 1997
Subjects
Control systems
Difference equations
Differential equations
Linear systems
Lyapunov method
Nonlinear equations
Physics
Prototypes
Stability analysis
System testing
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Summary:This paper collects work on the stability analysis of hybrid systems. The hybrid systems considered are those that combine continuous dynamics (represented by differential or difference equations) with finite dynamics, usually thought of as being a finite automaton. We review multiple Lyapunov functions as a tool for analyzing Lyapunov stability of general hybrid systems. Background results, the author's introductory work, and subsequent extensions are covered. Specializing to hybrid systems with linear dynamics in each constituent mode and linear jump operators, we review some key theorems of Barabanov-Staroshilov (1988), and give corollaries encompassing several recently-derived "stability by first approximation" theorems in the literature. We also comment on the use of computational tests for stability of hybrid systems, and the general complexity. The result is a tutorial on the state of the art in theory and computation of hybrid systems stability.
ISBN:0780341872
9780780341876
ISSN:0191-2216
DOI:10.1109/CDC.1997.650600