线性定常系统规范结构分解问题的研究  

Research Questions of Linear Time-invariant Systems Canonical Structural Decomposition

作　　者：蒋小平[1] 彭朝阳[1] 杨林璐 魏立彬 

机构地区：[1]中国矿业大学(北京)机电与信息工程学院,北京100083

出　　处：《数学的实践与认识》2017年第15期266-273,共8页Mathematics in Practice and Theory

基　　金：中央高校基本科研业务费专项资金项目(00-800015G2)

摘　　要：单输入单输出线性定常系统的状态空间按能控性和能观测性进行结构分解,能全面、完整的反映系统的各个子系统特性,理论上揭示状态空间的本质特征.通过规范性分解,不完全能控和不完全能观测的连续时间线性时不变系统可分解为"能控能观测","能控不能观测","不能控能观测","不能控不能观测"四个子空间,但是其分解后子空间的维度受非奇异变换矩阵P_c的影响.提出了一种约束变量的方法,用来选取P_c中列向量的规则,以控制原系统分解后子空间的表现形式.经实例验算,方法简单有效,具有一定的教学和理论意义.Single-input single-output linear time-invariant systems for structural decompo- sition of the state space based on the controllability and observability, reflecting the char- acteristics of the various subsystems comprehensively and completely, revealing the essential characteristics of the state space theoretically. By canonical decomposition, not fully able to control and incomplete can be observed continuous-time linear time-invariant systems decom- posed into four subspace： ＂controllable can be observable＂, ＂controllable but not observable＂, ＂observable but not controllable＂, ＂not observable and not controllable＂, but dimensional sub- space decomposition affected by nonsingular transformation matrix. This paper proposes a method of constrained variables, the rule used to select the column vector of Pc, control sub- space manifestations after the decomposition of the original system. After checking instances, this method is simple and effective, have certain teaching and theoretical significance.

关 键 词：线性定常系统 非奇异线性变换 规范分解 能控性 能观测 

分 类 号：O151.2[理学—数学]