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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.

Reviewer: T.Riismaa (Tallinn)

### 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 |

### Keywords:

limit cycles; manufacturing systems; logic controllers; hybrid dynamical systems; cyclic linear differential automata; linear discrete-time system; attractor; periodic trajectory; global stability
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\textit{A. V. Savkin} and \textit{A. S. Matveev}, Automatica 36, No. 5, 727--734 (2000; Zbl 0986.93043)

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### References:

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