Discrete Ingham type inequalities and simultaneous observability of strings or beams

Harmonic analysis has been an efficient tool in control theory for a long time, see, e.g., Russell [D.L. Russell, Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions, SIAM Rev. 20 (1978) 639-739] and its numerous references, Here we establish discrete Ingham type and Haraux type inequalities for exponential SLIMS satisfying a weakened gal) condition. They enable Lis to obtain discrete simultaneous observability theorems for systems of vibrating strings or beams. (c) 2008 Elsevier Inc. All rights reserved.