具外部扰动的变时滞不确定奇异系统的滑动模态控制

Sliding mode control for uncertain time-delays singular system with external disturbances

研究了含有多个变时滞的不确定奇异系统的滑动模态问题.该系统相比文献中已研究的系统更为复杂,具有多个变时滞,且分别含有匹配和不匹配的外部扰动项.通过对系统进行等价分解化为两个子系统,对分解后的系统进行切换函数的设计,再通过定义Lyapunov函数得到使得系统的滑模运动渐近稳定的充分条件.由此证明了所设计的滑模控制率能够保证状态轨迹在优先时间内被驱动到指定的切换面上且保持运动.设计过程简单,且结果以线性矩阵不等式呈现,相比文献中已有的结论更易于实现.最后通过例子验证结论的正确性.

This paper discusses the sliding mode control for uncertain time-delays singular system with external disturbances.The discussed system is more complicated than papers listed in the reference, for it has several delays, and both matching and mismatching external disturbances. Based on the transformation from the uncertain singular multi-delay-system to two subsystems, firstly we design the switching function such that system could be drift onto the sliding surface in limit time and maintains motion on it. After that we get the sufficient condition of asymptotic stabilization of sliding mode motion by defined the Lyapunovofunction. The design process is simple and the result is given by form of LMI so that the realization is more easy than papers listed in the reference. At last we take a numerical example to demonstrate the correctness of the results.