Tracking control for hybrid systems with state jumps using gluing function

In this paper, we propose a novel controller design technique to track a reference trajectory for a class of hybrid systems having state-triggered jumps. The idea is, by gluing start and end points of jumps in the state space, to change the domain into another domain where the state jumps disappear. After gluing, the hybrid systems can be considered as continuous or piecewise continuous dynamical systems without any state jumps. Therefore, it would be possible to construct tracking controllers for the hybrid systems through conventional design methods. The proposed technique guarantees that the state converges to the reference except the region where jumps occur or arrive at. Simulation results for various examples illustrate the effectiveness of the proposed approach.