广义Delta算子系统的非脆弱容许控制

Non-Fragile Admissible Control for Singular Delta Operator Systems

针对广义Delta算子系统的非脆弱控制问题,利用广义Delta算子系统容许的充要条件,给出系统广义二次容许的定义,以保证系统存在不确定时仍然容许,并采用线性矩阵不等式的方法,给出了广义Delta算子系统非脆弱状态反馈容许控制器存在的充分必要条件,同时利用线性矩阵不等式所得到的解,给出控制器的设计方法,使闭环系统广义二次容许,通过数值算例,对文中的理论结果进行仿真验证。仿真结果表明,当F=1,x1(0)=5以及F=-1,x1(0)=5的两种情况下,本文所设计的非脆弱控制器是可行有效的。因此,证明Delta算子方法在广义离散系统的非脆弱研究方面有很好的应用。

Regarding the problem of non-fragile control for singular delta operator systems, the the definition of generalized quadratical admissibility is given for uncertain singular delta operator systems based on a necessary and sufficient admissibility condition,and by means of linear matrix inequality（LMI）, a neces- sary and sufficient condition is given for the existence of a suitable non-fragile admissible controller. In the meantime, the design method of the controller is also presented in terms of the solution to the linear matrix inequality, which can ensure the corresponding closed-loop system generalized quadratically admissible. A numerical example is provided to demonstrate the effectiveness of the result in this paper. Simulation re sults show that when F=I ,：cl （0）=5 and F=-1 ,x1 （0）=5 ,the non-fragile controller designed in this paper is feasible and valid. Therefore,it proves the delta operator method has a good application in the research of non-fragile admissible control for singular discrete system.