Simple proofs are presented which show that hybrid boundary control systems are asymptotically, but not exponentially, stable. The asymptotic rates of decay of eigenvalues are determined analytically for both second and fourth-order systems.
Carrier, G. F., Krook, M., and Pearson, C. E., 1983, Functions of a Complex Variable: Theory and Technique, Hod Books, Ithaca, NY, p. 61.
Pointwise Stabilization in the Middle of the Span for Second Order Systems: Nonuniform and Uniform Exponential Decay of Solutions,”
SIAM J. of Applied Math., Vol.
Chen, G., Krantz, S. G., Ma, D. W., Wayne, C. E., and West, H. H., 1987b, “The Euler-Bernoulli Beam Equation with Boundary Energy Dissipation,” Operator Methods for Optimal Control Problems, S. J. Lee, ed., Marcel-Dekker, New York, pp. 67–96.
Lee, E. B., and You, Y. C., 1987, “On Stabilization of a Hybrid (String/Point Mass) System,” Proc. 5th International Conference on System Engineering, Dayton, OH, Sept., pp. 109–112.
Stabilization of a Hybrid System of Elasticity by Feedback Boundary Damping,”
Annali di Matematica Pura ed Application, Vol.
Decay Estimates of Solutions for a Hybrid System,”
European J. of Applied Math., Vol.
Zhu, W. D., and Mote, C. D., Jr., 1997, “Dynamic Modeling and Optimal Control of Rotating Euler-Bernoulli Beams,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL, published in this issue pp. 802–808.
This content is only available via PDF.
Copyright © 1997
by The American Society of Mechanical Engineers