Variable structure control of continuous-time system with sliding sector

Abstract For any control systems, it is shown that in the state space there exists a subset around a hyperplane, inside which a norm of the state decreases without any control action. Therefore it is possible to use this natural feature of control systems to design a VS controller. In this paper, such subset is named the sliding sector. An algorithm to design the sliding sector using Riccati equation is given for controllable systems. A variable structure (VS) controller with the sliding sector for continuous-time system is proposed. With the VS control law designed in the paper, the state will move to the inside of the sliding sector and the norm of the state, i.e. some Lyapunov function decreases in all of the state space. Therefore the VS controller with the sliding sector quadratically stabilizes the system. A rotational pendulum system is used as a simulation model. The simulation results show that the proposed VS controller is chattering-free and with good control performance.