带有离散和分布时滞不确定广义系统的鲁棒H_∞控制

Robust H∞ Control for Uncertain Singular Systems with Discrete and Distributed Delays

研究了带有离散和分布时滞不确定广义系统的鲁棒H∞控制问题.在给出使得系统正则、无脉冲、稳定且具有给定H∞性能界的时滞相关有界实引理的基础上,得到了系统鲁棒H∞状态反馈控制律存在的充分条件和直接的设计方法.所给结果均以线性矩阵不等式表示,且不含系统系数矩阵的分解.最后,通过数值例子说明了所给方法是有效的,且具有更小的保守性.

The problem of delay-dependent robust H∞ control for uncertain singular systems with discrete and distributed delays is discussed. A delay-dependent bounded real lemma （BRL） is presented to ensure the systems to be regular, impulse free and stable with H∞ performance condition. Based on the BRL ob- tained, the delay-dependent condition for the existence of robust H∞ state feedback controller is presented, and an explicit expression for the desired state feedback controller is also given. All the results obtained are formulated in terms of linear matrix inequalities （LMIs） and involving no decomposition of the system matrices. Numerical examples are given to demonstrate that the proposed method is effective and less con- servative than other methods available.