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

Authors
Journal
Automatica
0005-1098
Publisher
Elsevier
Publication Date
Volume
36
Issue
5
Identifiers
DOI: 10.1016/s0005-1098(99)00199-5
Keywords
  • Limit Cycles
  • Dynamic Systems
  • Nonlinear Systems
  • Stability Analysis
  • Manufacturing Systems
  • Logic Controllers
  • Automata Theory

Abstract

Abstract We introduce a special class of hybrid dynamical systems: cyclic linear differential automata (CLDA). We show that any CLDA can be reduced to a linear discrete-time system with periodic coefficients. 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 sufficient condition for global stability of CLDA is given. We apply our result to prove global stability of a flexible manufacturing system modelled as a switched server system.

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