线性分式不确定系统保成本控制及其鲁棒界

Guaranteed cost control and robust bound for linear fractional uncertain system

研究线性分式不确定系统的动态输出反馈保成本控制.采用线性矩阵不等式(LMI)方法证明了保成本控制器存在的充分必要条件等价于一个LMI可解性问题,通过该条件将求解闭环系统的成本函数上界的最小值问题转化为一个凸优化问题,利用该凸优化问题的解,得到动态输出反馈控制器的增益矩阵,并且给出了摄动参数允许最大摄动界的一种算法.

The dynamic output feedback guaranteed cost control for systems with linear fractional uncertainty was addressed.Based on linear matrix inequality(LMI),it was proved that necessary and sufficient condition for the existence of guaranteed cost controller was equivalent to the feasibility of a certain linear matrix inequality .A convex optimization problem was introduced to minimize the upper bound for the cost function of the closed-loop system,and the output feedback controllers were characterized by the solutions to this problem.By Finsler's lemma,an algorithm for finding a maximum perturbation bound for all admissbile perturbation parameters was also presented.