Algebraic and geometric properties of equilibria in cyclic switched dynamic systems

The analysis of some properties for the equilibria of switched dynamic systems is addressed. In particular, the geometric properties of the equilibrium region in state space and the algebraic properties of the equations defining it are studied. Based on fundamental results from algebraic geometry, the equilibria properties of switched dynamic systems are analyzed. This alternative approach allows to obtain information about the set of equilibrium points without explicitly computing it. This study is developed for three different formulations of switched dynamic systems, revealing some interesting algebraic and geometric relations in their corresponding equilibria. Some examples, including the case of a power converter, are presented for illustration purposes.