Existence and Stability of Equilibria for a Class of Hybrid Systems With Logical Effects

In this letter, a class of hybrid systems with logical effects is investigated. First, we give the algebraic form of the hybrid systems with the help of the semi-tensor product (STP, i.e., Cheng product). Next, a necessary and sufficient condition for the existence of equilibria is presented. Further, the local asymptotic stability and basins of attractors are discussed. Finally, some numerical examples are provided to demonstrate the validity of the theoretical results.