Analytic controllability of a linear hybrid system

In this paper, we consider a boundary control problem for a model of a flui d-structure hybrid system. This model has been introduced by Micu and Zuazu a in connection with the works of Banks et al. They have given explicit val ues for the spectral data in [S. Micu and E. Zuazua, SIAM J. Math. Anal., 2 9 (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 latt er paper, they use variable separation and Ingham inequalities to prove an observation estimate that implies, through the Hilbert uniqueness method, t hat initial data can be controlled within finite time. This paper improves these results by using a stronger form of Ingham inequality for low frequen cies. Indeed, we prove that any analytic function is controlled in a finite time whose dependence on the analyticity can be sharply estimated.