一类具有闭环极点约束的不确定线性系统的保性能控制

Guaranteed cost control of a class of uncertain linear systems with closed-loop disc pole constrains

主要研究了闭环系统的极点约束在一个给定圆盘中的保性能控制问题,基于线性矩阵不等式处理方法给出了状态反馈控制器存在的充要条件,并利用线性矩阵不等式的解给出了保性能控制器的设计方法,得到一个状态反馈控制器,使得对所有允许的不确定性闭环系统稳定,并且闭环性能指标值不超过某个确定的上界.最后以数值例子验证了结果的正确性.

We deal with the guaranteed cost control of a class of uncertain linear systems with closed-loop disc pole constrains. The existence of the guaranteed cost controller is shown to be equivalent to the feasibility of a certain linear matrix inequality, and the state feedback controller can be constructed in terms of the feasible solutions of this linear matrix inequality. A design procedure for state feedback controller is derived which renders the closed-loop systems to be stable and guarantees an upper bounded of the given performance cost for all admissible uncertainties. At last, an example illustrates the application of the proposed method.