Control and Stability of Generalized Bilinear Proportional Variable Structure System

Upon the basis of the law about single input bilinear constant value and proportion variable structure control and generalized bilinear constant value variable structure control systems,the control law of generalized bilinear variable structure with proportional to the state variables is studied.The ordering truncating operator Ωm is introduced to let the former m of components of state variables that absolute are larger in variable structure control law be proportional to the components and carry out the m of components to control the n of ones.The step of synthesis for generalized bilinear proportion variable srtucture control systems with many input using Lyapunov methods is proposed in detail.Conditions of stability about in these systems using Lyapunov Theorems of stability are presented.The result of computer simulation of a 3 -order systems is shown.