时滞区间广义系统的最优保成本控制

Optimal guaranteed cost control for interval singular systems with time-delay in state

研究了一类时滞区间广义系统的最优保成本控制问题.其中,系统矩阵和输入矩阵的各元素是未知的,但在某一确定的区间内变化.首先给出了时滞区间广义系统的一种等价描述形式,其次利用线性矩阵不等式方法,得到了问题有解的充要条件和状态反馈控制器的设计方法.设计的控制器不仅使得闭环系统广义二次稳定,而且最小化闭环性能指标的上界.最后举例说明了所给方法的正确性.

The problem of optimal guaranteed cost control was discussed for a class of interval singular systems with state delay. The elements in system matrix and input matrix are uncertain but vary with in a prescribed range. First, a kind of equivalent description of the interval singular systems with state delay is given. Further, a necessary and sufficient condition for the solvability of the problem is proposed in terms of linear matrix inequality（LMI）, and what is obtained is the desired state feedback controller which makes the closed-loop systems generalized quadratically stable and the minimization of the upper boundary of closed-loop performance index. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.