Stabilization via symmetry switching in hybrid dynamical systems (Q553476)

The authors consider hybrid dynamical systems involving the interaction of continuous dynamical behaviour and discrete event dynamics. In order to set up a mathematical environment for the modeling and analysis of this systems they make use of hybrid automata which are dynamical systems networked by a transition graph provided with rules supervising the discrete transition behaviour. From this set up they consider a subclass of dynamical systems called switched systems. They focus on the study of asymptotic stability of switched linear systems in the presence of symmetries. They introduce the concept of orbital switching to examine switching strategies that are induced by symmetries. They obtain sufficient conditions that guarantee asymptotic stability with respect to symmetry induced orbital switching. They illustrate their work through examples.