Boundary controllability of a linear hybrid system arising in the control of noise

SIAM Journal on Control and Optimization

Volumn 35, Issue 5, 1997, Pages 1614-1637

  Micu, Sorin ^a,b   Zuazua, Enrique ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSITY OF CRAIOVA   (Romania)

Author keywords

Aeromechanic structure interaction; Boundary control; Hyperbolic system

Indexed keywords

ACOUSTIC VARIABLES CONTROL; BOUNDARY VALUE PROBLEMS; CONTROLLABILITY; FOURIER TRANSFORMS; PROBLEM SOLVING;

BOUNDARY CONTROL; HYPERBOLIC SYSTEM; LINEAR WAVE EQUATIONS;

CONTROL SYSTEM ANALYSIS;

EID: 0031235389     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012996297972     Document Type: Article

References (18)

1. B. ALLIBERT, Contrôle analytique d'un modèle hybride fluide-structure, preprint, 1996.
2. G. AVALOS, The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustics, Abstract Appl. Anal., to appear.
3. G. AVALOS AND I. LASIECKA, A differential Riccati equation for the active control of a problem in structural acoustics, J. Optim. Theory Appl., to appear.
4. J. BALL AND M. SLEMROD, Nonharmonic Fourier series and the stabilization of distributed semi-linear control systems, Comm. Pure Appl. Math., XXXII (1979), pp. 555-587.
5. H. T. BANKS, W. FANG, R. J. SILCOX, AND R. C. SMITH, Approximation methods for control of acoustic/structure models with piezoceramic actuators, J. Intelligent Material Systems Structures, 4 (1993), pp. 98-116.
6. C. BARDOS, G. LEBEAU, AND J. RAUCH, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary, SIAM J. Control Optim., 30 (1992), pp. 1024-1065.
7. S. HANSEN AND E. ZUAZUA, Exact controllability and stabilization of a vibrating string with an interior point mass, SIAM J. Control Optim., 33 (1995), pp. 1357-1391.
8. A. HARAUX, Séries lacunaires et contrôle semi-interne des vibrations d'une plague rectangulaire, J. Math. Pures Appl., 68 (1989), pp. 457-465.
9. A. E. INGHAM, Some trigonometrical inequalities with applications to the theory of series, Math. Z., 41 (1936), pp. 367-369.
10. J. L. LIONS, Contrôlabilité exacte, perturbations et stabilization de systèmes distribués. Tome 1. Contrôlabilité exacte, Rech. Math. Appl. 8, Masson, Paris, 1988.
11. W. LITTMAN AND L. MARCUS, Exact boundary controllability of a hybrid system of elasticity, Arch. Rational Mech. Anal., 103 (1988), pp. 193-236.
12. S. MICU, Análisis de un modela híbrido bidimensional fluido-estructura, Ph.D. thesis, Universidad Complutense de Madrid, Spain, 1996.
13. S. MICU AND E. ZUAZUA, Propriétés qualitatives d'un modèle hybride bi-dimensionnel intervenant dans le contrôle du bruit, C. R. Acad. Sci. Paris Sér. I Math., 319 (1994), pp. 1263-1268.
14. S. MICU AND E. ZUAZUA, Asymptotics for the Spectrum of a Fluid/Structure Hybrid System Arising in the Control of Noise, preprint.
15. S. MICU AND E. ZUAZUA, Stabilization and periodic solutions of a hybrid system arising in the control of noise, in Proceedings of the IFIP TC7/WG-7.2 International Conference, Laredo, España, Lecture Notes in Pure and Applied Mathematics 174, Marcel Dekker, New York, 1996, pp. 219-230.
16. J. L. PUEL AND E. ZUAZUA, Exact controllability for a model of a multidimensional flexible structure, Proc. Roy. Soc. Edinburgh Sect. A, 123 (1993), pp. 323-344.
17. M. TUCSNAK, Regularity and exact controllability for a beam with piezoelectric actuators, SIAM J. Control Optim., 34 (1996), pp. 922-930.
18. E. ZUAZUA, Exact controllability for the semilinear wave equation in one space dimension, Ann. Inst. H. Poincaré Analyse Non Linéaire, 10 (1993), pp. 109-129.