Construction Method of Switching Hyperplane for Variable Structure Systems

가변구조계에 대한 스윗칭 초평면 설정의 한 방법

A construction method of a switching hyperplane for the Variable Structure Systems, which have robustness for parameter variations and noises in sliding mode is presented. The problem of composing a switching hyperplane is considered as a special case of the pole assignment for a closed-loop system. It is shown that the condition for constructing arbitrarily a switching hyperplane matrix C is equivalent to the controllability of the pair matrix(A, B) for the system, and then an algorithm of obtaining the switching hyperplane is proposed. It is also proved that zeros of the system are invariable in the sliding mode, and the stability for the system dynamic is equivalent to the stability of PA $\textit{ker}$ C. The applicability of the method proposed in the paper is shown by the simulation results for an example system.