广义Delta算子系统的耗散性分析与控制

针对线性广义离散系统的耗散性分析与耗散性控制问题,本文采用Delta算子离散化方法,对广义Delta算子系统进行耗散性研究,对该系统进行耗散性分析,得到了使广义Delta算子系统容许且严格耗散的充分必要条件,对于非容许且严格耗散的广义Delta算子系统,给出了该系统存在状态反馈严格耗散控制器的充分条件及耗散控制器的设计方法。同时借助MATLAB-LMI工具箱,对给出的数值算例进行计算和验证,验证结果表明,所得闭环系统容许且严格耗散,证明Delta算子方法在广义离散系统的耗散性研究中应用良好,其为广义离散系统其它性能的研究提供了新思路。

Dissipativity Analysis and Control of Linear Singular Delta Operator Systems

Aiming at the issue of singular discrete systems about dissipativity analysis and control, this pa- per applies a delta operator method to study and analyze the dissipativity of singular delta operator system. we obtain a necessary and sufficient condition that makes a linear singular delta operator system be admis- sible and strictly dissipative. As to these singular delta operator systems without admissibility and dissipa- tivity, a sufficient condition is derived for the existence of a state feedback strict dissipative controller, and the explicit expression of the corresponding controller is also presented. By using MATLAB-LMI tools, some numerical examples are provided to demonstrate the feasibility and effectiveness of the theoretical re- suits. It turns out that the close-loop system is admissible and strictly dissipative. These results suggest that the delta operator method makes a good application in the research of singular discrete systems about dissipativity. It provides a new way to research other properties of singular discrete system.