Abstract: This paper considers the non-fragile guaranteed cost control problem for a class of uncertain nonlinear systems with states time-delay.The Lyapunov stability theory and the LMI approach are applied to design a non-fragile guaranteed cost control law，which results that the closed-loop system is asymptotically stable and the system’s performance index is less than a determinate super bound.A convex optimization problem with LMI constraints is formulated to design the optimal non-fragile guaranteed cost controller for minimizing the performance index of the closed-loop uncertain system.Simulation results show the validity of the proposed control algorithm.

Key words: nonlinear systems, non-fragile guaranteed cost control, time-delay, Linear Matrix Inequation（LMI）

摘要： 研究了一类具有状态时滞的不确定非线性系统的非脆弱保成本控制问题。通过利用Lyapunov稳定性理论和线性矩阵不等式方法，设计非脆弱保成本控制律，使得闭环系统渐近稳定，并且系统的性能指标不超过某个确定的上界。通过求解一个具有线性矩阵不等式约束的凸优化问题来设计最优非脆弱保成本控制器，以使得闭环不确定系统的性能指标最小化。仿真结果验证了该控制算法的有效性。

关键词: 非线性系统, 非脆弱保成本控制, 时滞, 线性矩阵不等式（LMI）