不确定离散广义系统的保成本控制

针对一类具有范数有界时变参数不确定性的离散广义系统和二次成本函数,研究保成本控制律的设计问题。利用李雅普诺夫稳定性理论,得到了不仅使得闭环系统鲁棒二次稳定,而且闭环成本函数不超过某个确定上界的保成本控制存在的充分必要条件,并通过求解一个里卡蒂不等式给出了最优控制律的设计方法,最后通过数值例子说明方法的可行性。

Guaranteed cost control for uncertain discrete-time singular systems

Aimed at the discrete-time singular system possessing norm-bounded time-variant parameter uncertainty and a quadratic cost function,the problem of designing a guaranteed cost controller is considered in this paper.And by using Lyapunov stability theory,the necessary and sufficient condition is derived for the existence of a guaranteed cost controller,which not only can make a closed loop system robust quadratic stable but also can assure that its cost is not over a certain determinable upper bound.Then the designing method of optimum controller is formulated by solving Riccati inequation with parameters.Finally,an example is given to illustrate the feasibility of this method.