具有输入滞后的不确定系统的鲁棒H_∞控制

Robust H_∞ Controller for a Class of Uncertain Systems with Delayed Input

针对一类具有输入滞后的不确定系统,基于所谓的还原法,结合Lyapunov稳定性理论,讨论了其鲁棒H∞控制器设计问题.在零初始条件下,得到了该系统满足鲁棒H∞性能的一个充分条件,且控制器存在的充分条件由线性矩阵不等式组(LMIs)的形式给出,可以通过求解一个线性矩阵不等式组获得鲁棒H∞控制器,最后以一个具体算例说明了该方法的有效性.

For a class of uncertain systems with delayed input, the design of a robust H∞ controller is considered based on the so-called reduction method and Lyapunov stability theory. On condition that the initial value is zero, a sufficient condition is presented in the form of linear matrix inequalities （LMIs） for the existence of H∞ controller. The proposed controller not only stabilizes closed-loop uncertain systems, but also guarantees a prescribed norm bound. By solving the linear matrix inequalities （LMIs）, a robust H∞controller is obtained. Finally, an illustrative example is given to show the effectiveness of the proposed method.