广义线性系统的结构分类方法

A Structure Classification Method for Singular Linear Systems

基于受限等价变换的结构分析方法,提出实现多个矩阵的同时标准化的方法,从而得到广义系统的标准型,该方法使复杂的广义系统等价于多种简单的系统;根据标准型的特点,对分解后的多种简单广义系统进行细化分类;对不同类型的简单广义系统的控制方法进行研究,使复杂广义系统的控制问题转化为简单广义系统的控制问题。数值仿真结果表明,该方法对广义系统的结构的分类更细致具体,便于后续对广义系统的解、脉冲及其能控等方面进行更深入的研究,理论创新前景十分广阔。

We use a series of methods based on restricted equivalent transformation on the state space equation of singular linear systemsto obtain a standard form of the system architecture of the basis of matrix decomposition and matrix transformation. This method makes a complex singular system equivalent to multiple simple systems. According to the standard fealures of the decomposition of a broad variety of simple classification systems for refinement, we study the different types of simpler singular systems, and transform the problem of control a complex singular system into the problem of control several simple systems. The experiment result shows that such structure classification method on singular control systems is more specific and detailed. And it makes it easy for the study of singular system solution andimpulse and its controllability. It also has a wide theoretic prospective.