一般双线性比例变结构系统的控制及其稳定性

Control and Stability of Generalized Bilinear Proportional Variable Structure System

在单输入双线性常值变结构控制、比例变结构控制和一般双线性常值变结构控制系统的基础上，研究一般双线性比例变结构系统的控制策略，给出了控制结构图。采用状态反馈，定义排序截尾算子，使控制律与状态变量中前ｍ个绝对值较大的分量成比例，实现用ｍ个控制量对ｎ（ｎ≥ｍ）个被控量的控制。给出了用李亚普诺夫方法综合这类系统的详细步骤，根据李亚普诺夫稳定性定理得出了这类系统的稳定条件，根据这一条件选择比例系数并进行了仿真实验。

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 Ω m 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.