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Cyclic linear differential automata: A simple class of hybrid dynamical systems. (English) Zbl 0986.93043

A special class of hybrid dynamical systems, cyclic linear differential automata (CLDA), is introduced. It is shown 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 a system is a periodic trajectory. The CLDA is called globally stable if it has a periodic trajectory that attracts all other trajectories of the system. A necessary and sufficient condition for global stability of CLDA is given.

MSC:

93C65 Discrete event control/observation systems
93D20 Asymptotic stability in control theory
93C55 Discrete-time control/observation systems
37B15 Dynamical aspects of cellular automata
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