Variable Structure Control for a System with Mismatched Disturbances

입력과 매칭되지 않는 외란을 갖는 시스템에 대한 가변구조제어

For several decades, VSC has gained much attention as one of the useful design tools for handling the practical system with uncertainties or disturbances. Generally, the disturbances in the matching condition can be perfectly rejected via VSC; however, these in the mismatching condition are known to be hardly rejected. There have been some trials on it, in which the resulting controls in fact belong to the class of robust control guaranteeing disturbance ${\gamma}$-attenuation. Therefore, in this paper, we propose a new Variable Structure Control (VSC) for a system with mismatched disturbances. The proposed controller is composed of linear and nonlinear parts; the former plays a role in stabilizing the system and the latter takes care of attenuating the disturbances. The main contribution is to introduce the concept of switching-zone, rather than switching-surface, that is designed through piece-wise Lyapunov functions. The resulting non-convex conditions are formulated with an iterative linear programming algorithm, which provides an excellent performance of almost rejecting the disturbances.