Hybrid Control With Sliding Sector

This paper proposes a variable structure controller (VS) with sliding sector for hybrid systems. The extremum seeking control algorithm is used to find a Lyapunov function for the hybrid system. A sliding sector is defined as a subset of the state space inside which some norm of state decreases. In the paper, a sliding sector is designed for each subsystem of the hybrid system so that each state in the state space is inside at least one sliding sector with its corresponding subsystem, where the Lyapunov function found by the extremum seeking control is decreasing. A VS controller is designed to switch the hybrid system among subsystems to ensure the decrease of the Lyapunov function in the state space. The resulted VS control system is quadratically stable. Simulation results are given to show the efficiency of the proposed VS control system.