由弹簧和阻尼器连接的点质量链的能控性和能观性
On controllability and observability of chains formed by point masses connected with springs and dashpots
摘要：
我们考虑一个物理系统所构成的有限链的点质量连续连接的线性弹簧和阻尼器。在其中一个端点处，作用有与链条对齐的外部控制力，并且通过另一个端点的位置可以观察到系统。我们证明了，无论质点的个数是多少，如果弹性常数的序列与阻尼器常数的序列成正比，则在控制论意义下，该系统是完全能控的、完全能观的、完全可达的和完全可重构的.
英文摘要：
We consider a physical system constituted by a finite chain of point masses consecutively linked by linear springs and dashpots. At one of the end points acts an external control force aligned with the chain and the system is observable by the position of the other end point. We show that, whatever is the number of the point masses, if the sequence of the elastic constants is proportional to the sequence of the dashpot constants, then the mechanical system is completely controllable, completely observable, completely reachable and completely re-construictible, in the sense of control theory.
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