Stability and Sliding Mode of Proportional Variable Structure Control System with Bilinear

Upon the basis of the law about varible structure control with constant value,the control law of variable structure proportional to the state variables is chosen and Liapunov function method is employed.By applying Liapunov theorem and the conditions of existence and destination for sliding mode,the stability and sliding mode of a bilinear system with single input are studied.The theorem about stability and sliding mode for this kind of system is achieved.