A distributed parameter system consisting of two Euler-Bernoulli beams coupled in parallel is considered. It is shown that the system is uniformly exponentially stabilizable by an appropriate application of either distributed or boundary control. Strong stability is also established in both cases, although in the case of boundary control, the strong stability result is only proved for the situation in which both beams have identical dynamics.
Chen, G., 1979, "Energy decay estimates and exact boundary values controllability for the wave equation in a bounded domain," Journal de Mathématiques Pures et Appliqueés58(9), 249-274.
2.
Chen, G., Delfour, M.C., Crall, M.A., and Payre, G., 1987, "Modeling, stabilization and control of serially connected beams," SIAM J. Control Optim.25(3), 526-546.
3.
Chen, G., Fulling, A., Narcowich, F.J., and Sun, S., 1991, "Exponential decay of energy of evolution equations with locally distributed damping," SIAM J. Appl. Math.51, 266-301.
4.
Dafermos, C.M. and Slemord, M., 1973, "Asymptotic behavior of nonlinear contraction semigroups ," J. Funct. Anal.13, 97-106.
5.
Huang, F.L., 1993, "Strong asymptotic stability of linear dynamical systems in banach spaces," J. Diff. Eqs.104, 307-324.
6.
Kato, T., 1966, Perturbation Theory for Linear Operators, Springer-Verlag, New York.
7.
Komornik, V. and Zuazua, E., 1990, "A direct method for the boundary stabilization of the wave equation," Journal de Mathématiques Pures et Appliqueés69, 33-54.
8.
Lagnese, J., 1988, "Note on boundary stabilization of wave equations," SIAM J. Control Optim.26(5), 1250-1256.
9.
Littman, W., Markus, L., and Tou, Y., 1987, A Note on Stabilization and Controllability of a Hybrid Elastic System with Boundary Control, Report No. 87-103, University of Minnesota, Minneapolis, MN.
10.
Najafi, M., 1994, Energy Estimates and Stabilizability for Wave Equations in Bounded Domains Coupled in Parallel, Ph.D. dissertation, Wichita State University, Wichita, KS.
11.
Pazy, A., 1983, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York.
12.
Sarhangi, G.R., Najafi, M., and Wang, H., 1995, "The boundary stabilization of a linearized self-excited wave equation," Int. J. Systems Sci.26(11), 2125-2137.
13.
Timoshenko, S. and Young, D.H., 1974, Vibration Problems in Engineering, John Wiley, New York.
