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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