Variable Structure Control by Switching among Feedback Control Laws

This paper proposes a variable structure control algorithm, with which a system can be stabilized by switching the system control input among a set of feedback control laws. Each feedback control law is easy to be designed because it uses only one state variable with a fixed plus or minus feedback gain. For an n-order system, 2n feedback control laws are needed to realize the proposed variable structure control. The concept of the sliding sector is used in the paper to show that there exists an area for the system with each feedback control law, inside which a Lyapunov function decreases with the control law although the system may not be stabilized by it alone. A common Lyapunov function for all control law exists if the system is controllable. Based on the extremum seeking control algorithm, a sliding mode is defined such that the common Lyapunov function tracks a pre-determined decreasing function. Thus a variable structure control rule is designed such that the common Lyapunov function decreases in every period when the control input is switched once through all feedback control laws. The proposed variable structure control system is quadratically stable. Simulation results are given to show the convergence of the proposed variable structure control algorithm