Analytic Controllability of a Linear Hybrid System

Abstract

In this paper, we consider a boundary control problem for a model of a fluid-structure hybrid system. This model has been introduced by Micu and Zuazua in connection with the works of Banks et al. They have given explicit values for the spectral data in [S. Micu and E. Zuazua, SIAM J. Math. Anal., 29 (1998), pp. 967--1001] and results for the control problem in [S. Micu and E. Zuazua, SIAM J. Control. Optim., 35 (1997), pp. 1614--1637]. In the latter paper, they use variable separation and Ingham inequalities to prove an observation estimate that implies, through the Hilbert uniqueness method, that initial data can be controlled within finite time. This paper improves these results by using a stronger form of Ingham inequality for low frequencies. Indeed, we prove that any analytic function is controlled in a finite time whose dependence on the analyticity can be sharply estimated.