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We consider a physical system constituted by a finite chain of point massesconsecutively linked by linear springs and dashpots. At one of the end pointsacts an external control force aligned with the chain and the system isobservable by the position of the other end point. We show that, whatever isthe number of the point masses, if the sequence of the elastic constants isproportional to the sequence of the dashpot constants, then the mechanicalsystem is completely controllable, completely observable, completely reachableand completely re-construictible, in the sense of control theory.

On controllability and observability of chains formed by point masses connected with springs and dashpots