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Cyclic linear differential automata: a simple class of hybrid dynamical systems

โœ Scribed by Andrey V. Savkin; Alexey S. Matveev

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
201 KB
Volume
36
Category
Article
ISSN
0005-1098

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โœฆ Synopsis

We introduce a special class of hybrid dynamical systems: cyclic linear di!erential automata (CLDA). We show that any CLDA can be reduced to a linear discrete-time system with periodic coe$cients. Any CLDA has no equilibrium points. Therefore, the simplest attractor in such system is a periodic trajectory. We call a CLDA globally stable if it has a periodic trajectory which attracts all other trajectories of the system. A necessary and su$cient condition for global stability of CLDA is given. We apply our result to prove global stability of a #exible manufacturing system modelled as a switched server system.

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