不确定时滞系统的鲁棒H∞控制

基于Lyapunov稳定性理论，研究一类同时具有状态非线性不确定和线性不确定时变时滞系统的鲁棒控制器的设计问题。在非线性不确定性满足增益有界条件下，得到该类时变时滞系统依赖于时变延迟导数的最大值的满足鲁棒H∞性能的一个充分条件。通过求解一个线性矩阵不等式-LMI，即可获得鲁棒H∞控制器。给出的两个具体算例说明该方法的有效性。

Robust H∞ Controller Design for Time- delay Systems with Uncertainty

In this paper, Robust H∞ state feedback controller design is considered for linear delay system with linear uncertainty and nonlinear uncertainty based on Lyapunov stability theory. On condition that the nonlinear uncertain functions are gain bounded, a sufficient condition, which is dependent on the maximum value of the time derivative of time- varying delay, is presented for the existence of H∞ controller. The proposed controller not only stabilizes closed - loop uncertain systems but also guarantees a prescribed H∞ norm bound of closed- loop transfer matrix from the disturbance to controlled output. By solving a linear matrix inequation, we can obtain the robust H∞ controller. Two illustrative examples are given to show the effectiveness of the proposed method.