Shape optimization of piezoelectric sensors or actuators for the control of plates

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1. [1] G. Allaire, Shape optimization by the homogenization method. Springer-Verlag, New York (2002). Zbl0990.35001MR1859696
2. [2] H.T. Banks, R.C. Smith and Y. Wang, Smart material structures, modelling, estimation and control. Res. Appl. Math. Masson, Paris (1996). Zbl0882.93001
3. [3] D. Chenais and E. Zuazua, Finite Element Approximation on Elliptic Optimal Design. C.R. Acad. Sci. Paris Ser. I 338 729–734 (2004). Zbl1052.65059
4. [4] M.J. Chen and C.A. Desoer, Necessary and sufficient conditions for robust stability of linear distributed feedback systems. Internat. J. Control 35 (1982) 255–267. Zbl0489.93041
5. [5] R.F. Curtain and B. Van Keulen, Robust control with respect to coprime factors of infinite-dimensional positive real systems. IEEE Trans. Autom. Control 37 (1992) 868–871. Zbl0760.93061
6. [6] R.F. Curtain and B. Van Keulen, Equivalence of input-output stability and exponential stability for infinite dimensional systems. J. Math. Syst. Theory 21 (1988) 19–48. Zbl0657.93050
7. [7] R.F. Curtain, A synthesis of Time and Frequency domain methods for the control of infinite dimensional systems: a system theoretic approach, in Control and Estimation in Distributed Parameter Systems, H.T. Banks Ed. SIAM (1988) 171–224. 
8. [8] R. Datko, Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks. SIAM J. Control Optim. 26 (1988) 697–713. Zbl0643.93050
9. [9] E. Degryse, Étude d’une nouvelle approche pour la conception de capteurs et d’actionneurs pour le contrôle des systèmes flexibles abstraits. Ph.D. Thesis, Université de Technologie de Compiègne, France (2002). 
10. [10] P.H. Destuynder, I. Legrain, L. Castel and N. Richard, Theoretical, numerical and experimental discussion on the use of piezoelectric devices for control-structure interaction. Eur. J. Mech A/solids 11 (1992) 181–213. 
11. [11] B.A. Francis, A Course in $H_{\infty }$ Control Theory. Lecture notes in control and information sciences. Springer-Verlag Berlin (1988). Zbl0624.93003
12. [12] P. Freitas and E. Zuazua, Stability results for the wave equation with indefinite damping. J. Diff. Equations 132 (1996) 338–352. Zbl0878.35067
13. [13] J.S. Freudenberg and P.D. Looze, Right half plane poles and zeros and design tradeoffs in feedback systems. IEEE Trans. Autom. Control 30 (1985) 555–565. Zbl0562.93022
14. [14] J.S. Gibson and A. Adamian, Approximation theory for Linear-Quadratic-Gaussian control of flexible structures. SIAM J. Control Optim. 29 (1991) 1–37. Zbl0788.93027
15. [15] A. Haraux, Systèmes dynamiques dissipatifs et applications. Masson, Paris (1990). Zbl0726.58001MR1084372
16. [16] P. Hébrard and A. Henrot, Optimal shape and position of the actuators for the stabilization of a string. Syst. Control Lett. 48 (2003) 199–209. Zbl1134.93399
17. [17] P. Hébrard and A. Henrot, A spillover phenomenon in the optimal location of actuators. SIAM J. Control Optim., to appear. Zbl1083.49002MR2177160
18. [18] C. Inniss and T. Williams, Sensitivity of the zeros of flexible structures to sensor and actuator location. IEEE Trans. Autom. Control 45 (2000) 157–160. Zbl0973.93006
19. [19] S. Jaffard, M. Tucsnak and E. Zuazua, Singular internal stabilization of the wave equation. J. Differential Equations 145 (1998) 184–215. Zbl0920.35029
20. [20] T. Kato, Perturbation theory for linear operators. Springer-Verlag, Berlin (1980). Zbl0435.47001
21. [21] B. van Keulen, $H_{\infty }$ control for distributed parameter systems: a state-space approach. Birkaüser, Boston (1993). Zbl0788.93018MR1269323
22. [22] I. Lasiecka and R. Triggiani, Non-dissipative boundary stabilization of the wave equation via boundary observation. J. Math. Pures Appl. 63 (1984) 59–80. 
23. [23] D.G. Luenberger, Optimization by Vector Space Methods. John Wiley and Sons, New York (1969). Zbl0176.12701MR238472
24. [24] F. Macia and E. Zuazua, On the lack of controllability of wave equations: a Gaussian beam approach. Asymptotic Analysis 32 (2002) 1–26. Zbl1024.35062
25. [25] M. Minoux, Programmation Mathématique: théorie et algorithmes, tome 2. Dunod, Paris (1983). Zbl0546.90056MR714151
26. [26] O. Morgül, Dynamic boundary control of an Euler-Bernoulli beam. IEEE Trans. Autom. Control 37 (1992) 639–642. 
27. [27] S. Mottelet, Controllability and stabilization of a canal with wave generators. SIAM J. Control Optim. 38 (2000) 711–735. Zbl0966.76015
28. [28] V.M. Popov, Hyperstability of Automatic Control Systems. Springer, New York (1973). 
29. [29] F. Shimizu and S. Hara, A method of structure/control design Integration based on finite frequency conditions and its application to smart arm structure design, Proc. of SICE 2002, Osaka, (August 2002). 
30. [30] V.A. Spector and H. Flashner, Sensitivity of structural models for non collocated control systems. Trans. ASME 111 (1989) 646–655. Zbl0705.73154
31. [31] M. Tucsnak and S. Jaffard, Regularity of plate equations with control concentrated in interior curves. Proc. Roy. Soc. Edinburg A 127 (1997) 1005–1025. Zbl0889.35059
32. [32] Y. Zhang, Solving Large-Scale Linear Programs by Interior-Point Methods Under the MATLAB Environment. Technical Report TR96-01, Department of Mathematics and Statistics, University of Maryland, Baltimore, MD (July 1995). Zbl0916.90208

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