Controller Design of Hybrid Systems

Book chapter, 1997

In this paper we present two strategies to design a hybrid controller for a system described by several nonlinear vector fields. Besides the overall goal to find a controller that stabilizes the closed-loop hybrid system, the selection will also be made in such a way that an exponentially stable closed-loop system is obtained. The design strategies are based on stated stability and exponential stability theorems for hybrid systems. The first approach results in regions where it is possible to change vector fields guaranteeing (exponential) stability of the closed-loop hybrid system. The second design strategy utilizes the fact that a system is (exponentially) stable if it is always possible to choose a vector field that points in a direction such that the trajectory approaches the equilibrium point. These conditions can be verified by solving a linear matrix inequality (LMI) problem.