Cyclic linear differential automata: A simple class of hybrid dynamical systems
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.
scientific article; zbMATH DE number 1441460