广义Delta算子系统的输出反馈H_∞控制

Output Feedback H_∞ Control for Singular Delta Operator Systems

为给广义Delta算子系统设计合理的静态输出反馈和动态输出反馈控制器,以保证相应的闭环系统容许且具有H_∞性能指标γ,本文研究广义Delta算子系统的输出反馈H_∞控制问题。利用矩阵不等式方法,分别得到了广义Delta算子系统存在静态和动态输出反馈H_∞控制器的充分必要条件,并利用矩阵不等式的解给出了相应控制器的构造方法,同时通过数值算例对本文的理论结果进行验证。验证结果表明,按照本文方法所设计的静态和动态输出反馈控制器确实均能保证所得的闭环系统是容许的,且具有H_∞性能指标γ,因此本文的控制器设计方法是有效且可行的。该研究具有实际意义。

In order to design reasonable static and dynamic output feedback controllers for singular Delta operator systems to ensure that the corresponding closed-loop systems are admissible and have a prescribed H_∞ performance indexγ,this paper deals with the problem of output feedback H_∞control for singular Delta operator systems.By using the method of matrix inequalities,necessary and sufficient conditions for the existence of suitable static and dynamic output feedback H_∞ controllers are presented,respectively.Moreover,the design methods of the corresponding controllers are obtained based on the solutions to matrix inequalities and a numerical example is given to demonstrate the theoretical results in this paper.The results showed that the designed static and dynamic output feedback controllers according to the method in this paper can indeed ensure that the closed-loop systems are admissible and have H_∞ performance indexγ.Thus,the controller design methods in this paper are indeed effective and feasible.The study has practical significance.