Non-structural controllability of linear elastic systems with structural damping

摘要

This paper proves that any initial condition in the energy space for the plate equation with square root damping zeta - rho Delta zeta + Delta(2)zeta = u on a smooth bounded domain, with hinged boundary conditions = A = 0, can be steered to zero by a square integrable input function u supported in arbitrarily small time interval [0, T] and subdomain. As T tends to zero, for initial states with unit energy norm, the norm of this u grows at most like exp(C-p/T-p) for any real p > 1 and some C-p > 0. Indeed, this fast controllability cost estimate is proved for more general linear elastic systems with structural damping and non-structural controls satisfying a spectral observability condition. Moreover, under some geometric optics condition on the subdomain allowing to apply the control transmutation method, this estimate is improved into p = 1 and the dependence of Cp on the subdomain is made explicit. These results are analogous to the optimal ones known for the heat flow. (c) 2006 Elsevier Inc. All rights reserved.