AbstractRecently, the control engineers interest turns upon material with structural damping, such as hysteretic effects in elastoplastic systems 27 and flexible space structures 30and in particular with damping due to the viscoelastic nature of the material, in the sense of Kelvin, 7, 12. The reason for this renewed interest is the possibility of constructing finite rank compensators with small spillover in the observation 1, 5, 11, 25.However, a control theory for the infinite system does not seem to exist in the literature. It is shown that the trajectories, initially in a certain subspace, can be steered to rest in any timeT>0 using distributed load controlsThe reesults are partially contained in 19.. Furthermore, and perhaps more interesting, theL2(0,T,H)‐norm of the control decreases asTincreases. This gives rise to the problem of time‐optimal‐controllability and the correlation to the problem of minimum norm controllability.It is shown that the time‐optimal control is characterized by a weak “bang‐bang
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