不确定线性奇异系统的有限时间控制

Finite time control of an uncertain linear singular system with a time-varying disturbance

针对具有时变外部扰动的不确定线性奇异系统,研究基于状态反馈的有限时间控制问题,系统的状态矩阵和输入矩阵均含有范数有界不确定项。利用Lyapunov泛函方法和线性矩阵不等式(LMI)工具,给出了不确定奇异系统经由状态反馈的有限时间有界(FTB)的充分条件。这些充分条件都可转化为线性矩阵不等式可行性问题。并通过一个数值实例说明了该方法的有效性。

The finite time control problem was studied based on the state-feedback control for an uncertain linear singular system with exogenous disturbance, of which the state matrix and input matrix have norm-bounded uncertainties. By the Lyapunov functional method and linear matrix inequality （LMI） technique, the sufficient conditions of finite time boundedness （FIB） for the singular system via state feedback controller were provided. Then, the conditions were reduced to feasibility problems involving linear matrix inequalities （LMIs）. Finally, a numerical example was given to illustrate the validity of this proposed method.