Feedback stabilization of “hybrid” bilinear systems
Authors:
M. Slemrod and E. L. Rogers
Journal:
Quart. Appl. Math. 44 (1986), 589-599
MSC:
Primary 93D15; Secondary 93C20
DOI:
https://doi.org/10.1090/qam/860908
MathSciNet review:
860908
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Abstract: This paper considers the problem of stabilizing a control system governed by a combination of partial and ordinary differential equations. The partial differential equations govern the evolution of the system in the interior of some spatial domain, and the ordinary differential equations describe the evolution of the boundary data; the control enters through the boundary ordinary differential equations in a bilinear fashion. We provide sufficient conditions for feedback stabilization of such “hybrid” systems. Two examples to wave equations with dynamic boundary conditions are provided.
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J. A. Burns and E. M. Cliff, On control and identification of hybrid systems, AIAA Symposium on Dynamics and Control of Large Space Structures, Blacksburg, Virginia (June, 1981)
J. M. Ball and M. Slemrod, Nonharmonic Fourier series and the stabilization of distributed semi-linear control systems, Comm. Pure Appl. Math. XXXII, 555–587 (1979)
J. M. Ball and M. Slemrod, Feedback stabilization of distributed semilinear controls, Appl. Math. Optim. 5, 169–179 (1979)
K. Yosida, Functional Analysis, Springer-Verlag, New York (1971)
P. Morse and K. U. Ingard, Theoretical Acoustics, McGraw-Hill, New York (1968)
J. T. Beale, Spectral properties of an acoustic boundary condition, Indiana Univ. Math. J. 25, 895–917 (1975)
R. E. O’Brien, Energy decay in weakly locally reacting boundary value problems, Indiana Univ. Math. J. (in press)
A. S. Besicovitch, Almost Periodic Functions, Dover, New York (1954)
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Article copyright:
© Copyright 1986
American Mathematical Society
