具有α-稳定性的线性不确定时滞系统鲁棒H_∞控制

Robust H_∞ control with an αstability constraint for linear uncertain time-delay systems

针对一类具有时变状态时滞和参数不确定性的线性不确定时滞系统,研究了闭环极点具有α-稳定性限制的鲁棒H∞控制器设计问题.对所有容许的不确定,首先给出判断系统鲁棒α-稳定且具有干扰衰减γ的充分条件;而后基于线性矩阵不等式方法,分别提出了状态反馈和动态输出反馈控制器存在的充分条件及相应的控制器设计方法.数值算例验证了所给结果的有效性.

The problem of robust H∞ control satisfying some α - stability constraints on the closed-loop poles for a class of uncertain systems with time delay is investigated in this paper. The system under consideration involves time-varying state time delay and parameter uncertainties. For all admissible uncertainties, a sufficient condition is derived in which the prescribed level on disturbance attenuation ,γ and the α-stability constraints are still preserved. Furthermore, the sufficient condition for the existence of the solutions to the problem via state feedback control and output feedback control and the design of control are derived in terms of linear matrix inequalities （LMI）. A numerical example is provided to demonstrate the validity of the presented method.