Some Questions on Kalman Standard Decomposition of Linear Time-Invariable System
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摘要: 证明了线性时不变系统一般不能通过先可控分解,再分别对可控和不可控子系统进行可观分解而得到Kalman标准型.并讨论了在4个子空间< A|β >∩η、< A|β >∩η⊥、< A|β >⊥∩η和< A|β >⊥∩η⊥中取一组基,构造一个化系统为Kalman标准型的非奇异变换的可能性.最后,证明了在一定条件下存在一个正交变换,可将线性时不变系统化为Kalman标准型.
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关键词:
- 线性系统 /
- 可控性 /
- 可观测性 /
- Kalman标准分解
Abstract: It is shown that for a linear time-invariable system,its Kalman canonical form can not be obtained by decomposing the system into its controllable canonical form,and then decomposing its controllable and uncontrollable subsystems into their observable canonical form,respectively.The possibility is discussed to construct a non-singular transformation which transforms the system to its Kalman canonical form through choosing a basis in < A|β >∩η,< A|β >∩η⊥,< A|β >⊥∩η and < A|β >⊥∩η⊥ .Finally ,it is proved that the system can be transformed to its Kalman canonical form using an orthogonal transformation under appropriate conditions.-
Key words:
- linear systems /
- controllability /
- observability /
- Kalman canonical decomposition
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[1] 胡寿松.自动控制原理[M].北京:国防工业出版社,1994. [2]郑大钟.线性系统理论[M].北京:清华大学出版社,1992. [3]段广仁.线性系统理论[M].哈尔滨:哈尔滨工业大学出版社,1996. [4]陈际达.线性控制系统[M].长沙:中南工业大学出版社,1987. [5]赵纯均,詹一辉.控制理论基础[M].北京:清华大学出版社,1991. [6]赵 玖.线性系统理论[M].峨眉:西南交通大学出版社,1988. [7]戴忠达.自动控制理论基础[M].北京:清华大学出版社,1991. [8]王照林.现代控制理论基础[M].北京:国防工业出版社,1990. [9]胡克定,郑卫新.线性多变量系统的理论与设计[M].南京:东南大学出版社,1991. [10] 胡寿松.自动控制原理习题集[M].北京:国防工业出版社,1990. [11]张志方,孙长胜.线性控制系统教程[M].北京:科学出版社,1993. [12]程 鹏.线性系统理论[M].北京:北京航空航天大学出版社,1987. -
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