Overview
ABSTRACT
This paper provides an overview of hybrid dynamical systems, namely systems that comprise continuous and discrete dynamics. After presenting a mathematical framework that allows describing this class of systems, the key ideas behind the solution and stability concepts are presented mathematically and illustrated by examples. Some sufficient conditions for proving global uniform asymptotic stability are then proposed, by relying on Lyapunov functions, possibly associated with the LaSalle invariance principle.
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Read the articleAUTHORS
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Isabelle QUEINNEC : Research Director - LAAS, CNRS, Toulouse, France
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Sophie TARBOURIECH : Research Director - LAAS, CNRS, Toulouse, France
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Luca ZACCARIAN : Research Director - LAAS, CNRS, Toulouse, France and University of Trento, Italy
INTRODUCTION
Dynamical systems are generally classified according to whether they evolve continuously, in which case they are called continuous-time dynamical systems, or discretely, in which case they are called discrete-time dynamical systems. These two classes of systems have been studied extensively in the literature, but usually independently (see for example , ), using differential equations for continuous systems and difference equations for discrete systems. There are, however, many physical systems that combine both types of behavior, such as digitally controlled mechanical systems, or electronic circuits that combine analog and digital components. Similarly, dynamic systems with impacts and event-based systems, to name but two examples, require an adequate combination of behaviors described by differential equations and behaviors described by difference equations. Social networks and their studies can be seen as another field of application for hybrid dynamical systems (see, for example, ). For more details and examples, the reader can consult Chapter 1 of .
Reset control systems are another class of systems that mix continuous dynamics and discrete events
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KEYWORDS
stability | Hybrid dynamical systems | Attractor | Reset systems
A journey with hybrid dynamical systems
Modeling hybrid dynamic systems
Bibliography
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