Abstract: For uncertain time-varying linear delay systems with interval which is known and the lower limit is not zero, the problem of non-fragile robust [H∞] controller design is studied, based on Lyapunov stability theory and linear matrix inequality. By constructing an appropriate type of Lyapunov-Krasovskii function, combining with a new method of integral inequality, to get the time delay system is asymptotically stable and satisfy the [H∞] performance index of delay-dependent sufficient conditions. Then a class of non-fragile robust [H∞] state feedback controller of low conservative controllers based on an Improved Cone Complementary Linearization（ICCL） algorithm can be designed. A numerical example is given to illustrate the effectiveness of the design approach.

Key words: uncertain time-varying delay systems, non-fragile, robust [H∞] control, integral inequality, linear matrix inequalities

摘要： 基于Lyapunov稳定性理论和线性矩阵不等式方法，研究一类时滞区间已知且下限不为零的不确定时变时滞系统的非脆弱鲁棒[H∞]控制器设计问题，通过构造合理的Lyapunov-Krasovskii函数，结合一种新的积分不等式的方法，得到该类时滞系统渐近稳定且满足[H∞]性能指标的时滞相关充分条件，并基于改进的锥补线性化迭代算法（Improved Cone Complementary Linearization，ICCL）给出一种具有低保守型的非脆弱鲁棒[H∞]状态反馈控制器的设计方法，仿真结果说明了该控制器设计方法的有效性。

关键词: 不确定时变时滞系统, 非脆弱, 鲁棒H&infin, 控制, 积分不等式, 线性矩阵不等式