双线性变结构控制系统滑动模态方程的稳定性分析

Stability’s Analyze of Sliding Mode Equation For Bilinear Variable Structure Control System

使用等价控制方法构成双线性变结构控制系统的滑动模态方程。该方程右边的函数在实数域内不连续，是一个高度非线性微分方程组。分析了这类方程的特殊性，提出了“状态深阱”的概念。研究这类方程的稳定性，给出了使用庞克莱－李亚普诺夫第一近似定理的附加条件。讨论了一个四阶系统在具有两个切换面时的滑动模态方程的限定范围稳定问题，给出了数字例子的计算机仿真结果。

Equations of sliding mode for bilinear variable structure control system are structured by employing method of equivalent control.The equations are extra nonlinear differential equations.The dexter function is not continuous in field of real number.A particularity of the equations is analyzed.The conception of ‘state deep trap’is put forward.The accessory conditions by using theorem of first approximation are presented,when the stability of equations is studied.The stability problem of definite range in the sliding mode equations,which is a 4 orde system with two switching surfaces,is discussed and the result of computer simulation for numbel examples is shown.