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

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.