Simplified conditions of initial observability for infinite-dimensional second-order damped dynamical systems

In the paper, the initial observability of abstract second-order infinite-dimensional dynamical systems is considered. Two cases of observation operator are explored. First, the observation operator is assumed to be bounded. Then results are extended to more general class of observations related to the observation operators that are assumed to be bounded with respect to square root of elasticity operator which covers the case of some unboundedness in observation. Using the frequency-domain method it is proved, that initial observability of second-order system under discussion can be verified by the initial observability conditions for the corresponding simplified first-order system. General results are then applied for initial observability investigation of infinite dimensional systems described by partial differential equations modelling flexible mechanical structures. Some special cases are also discussed and practical comments and remarks are given. The paper extends earlier results on initial observability for a class of infinite-dimensional second-order abstract dynamical systems.