时变不确定多时滞连续系统的最优保成本控制

针对一类同时具有状态多时滞和输入多时滞的时变不确定连续多时滞系统。研究保成本状态反馈控制器的设计。假定其中的时变不确定性项是范数有界的，但不需要满足匹配条件，通过构造改造的Lyapunov函数和线性矩阵不等式（LMI）方法，给出系统满足保性能指标的一个充分条件，仅通过求解一个相应的线性矩阵不等式，就可得到保性能控制器使得闭环系统的一个保成本函数对所有允许的不确定参数有上界。通过求解凸优化问题得到最优保性能控制器，最后用数值例子说明该方法的有效性。

Optimal Guaranteed Cost Control for Uncertain Continuous Multi-time-varying Delay Systems

This paper studies the problem of guaranteed cost control for a class of time- varying uncertain continuous multi - time - delay systems with both state and input delays. Suppose that the time - varying uncertain parameters are norm- bounded, but the matched conditions are not required to satisfy. A new sufficient condition of satisfying guaranteed cost index is given for the systems by constructing Lyapunov function and linear matrix inequalities approach. Guaranteed cost controllers can be obtained only from solving corresponding linear matrix inequalities such that a guaranteed cost function for the closed- loop systems has an upper bound irrespective of all admissible parameters uncertainties. Optimal guaranteed cost controllers can be obtained from solving corresponding convex optimization. Furthermore, a numerical example is given to show the potential of the proposed techniques.