不确定非线性离散时滞系统的可靠保成本控制

针对一类不确定非线性离散时滞系统，研究了当执行器发生故障情况下的可靠保成本控制器设计问题.通过设计一个无记忆状态反馈可靠保成本控制律，使闭环系统渐近稳定，并且闭环性能指标不超过某个确定的上界.利用Lyapunov稳定性理论和线性矩阵不等式（LMI）方法，给出了可靠保成本控制律存在的条件.通过求解由一组线性矩阵不等式所表示的凸优化问题，可以得到使得闭环系统保成本上界最小的可靠保成本控制器.最后通过仿真实例说明方法的正确性.

Reliable guaranteed cost control for uncertain nonlinear discrete-time systems with state delay

The reliable guaranteed cost control problem for a class of uncertain nonlinear discrete-time systems with state delay and actuator failures is discussed.This problem is applied to design a memoryless state feedback reliable guaranteed control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties.Based on the Lyapunov stability theory and the linear matrix inequality(LMI) approach,the sufficient conditions for the existence of such controller are derived.The optimal reliable guaranteed cost controllers with minimum guaranteed cost for closed-loop systems are designed based on the solution of a convex problem in terms of LMIs.A numerical example is given to illustrate the proposed method.