不确定奇异系统的有限时间H_∞控制

Finite Time H_∞ Control for Uncertain Singular Systems

针对一类在有限时间下的线性奇异系统,同时考虑参数不确定性和有限外部扰动影响,研究了系统基于状态反馈控制器的鲁棒H∞控制问题。首先通过构造合适的Lypunov函数,利用线性矩阵不等式方法给出了线性广义系统有限时间有界且H∞范数有界的充分条件,在此基础上讨论线性广义系统的H∞状态反馈控制,给出了控制器存在的充分条件,同时给出了控制器的具体设计方法,控制器可由线性矩阵不等式解得。最后的数值算例说明了所提出方法的可行性和有效性。

For a class of singular systems with finite time in consideration of both parameter uncertainties and external disturbance with limited energy, the problem of robust H∞ control for system with state feedback controller is discussed. Based on Lyapunov functional and LMIs, the conditions for the linear singular system to be finite-time bounded and H∞ norm bound constraint are given in the form of matrix inequalities. Furthermore, one sufficient condition for the existence of an H~ state feedback controller is shown. The controller can be obtained via solving LMIs. Finally, an example is given to illustrate the validity of the proposed method.