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Control via decoupling of a class of second order linear hybrid systems
1. | Department of Mathematics, 460 McBryde Hall, Virginia Tech, Blacksburg, VA 24060 |
References:
[1] |
M. D. Aouragh and N. Yebari, Riesz basis approach and exponential stabilization of a nonhomogeneous flexible beam with a tip mass, Int. J. Math. & Stat., 7 (2010), 46-53. |
[2] |
S. Avdonin and S. Ivanov, Families of Exponentials: The Method of Moments in Controllability Problems for Distributed Parameter Systems, Cambridge University Press, Cambridge, New York, Melbourne, 1995. |
[3] |
M. S. Azam, N. Singh, A. Iyer and Y. P. Kakad, Detumbling and reorientation maneuvers and stabilization of NASA SCOLE system, IEEE Trans. Aerosp. & Electr. Syst., 28 (1992), 80-91.
doi: 10.1109/7.135434. |
[4] |
C. Baiocchi, V. Komornik and P. Loreti, Théorèmes du type Ingham et application à la théorie du contrôle, C. R. Acad. Sci. Paris Sér. I, Math., 326 (1998), 453-458.
doi: 10.1016/S0764-4442(97)89791-1. |
[5] |
W. E. Boyce and G. H. Handelman, Vibrations of rotating beams with tip mass, Angew. Math. & Phys., 12 (1961), 369-392.
doi: 10.1007/BF01600687. |
[6] |
F. Conrad and Ö. Morgül, On the stabilization of a flexible beam with a tip mass, SIAM J. Control. & Opt., 36 (1998), 1962-1986.
doi: 10.1137/S0363012996302366. |
[7] |
M. Grobbelaar-Van Dalsen, Uniform stability for the Timoshenko beam with tip load, J. Math. Anal. & and Appl., 361 (2010), 392-400.
doi: 10.1016/j.jmaa.2009.06.059. |
[8] |
B.-Z. Guo, Riesz basis approach to the stabilization of a flexible beam with a tip mass, SIAM J. Control. & Opt., 39 (2001), 1736-1747.
doi: 10.1137/S0363012999354880. |
[9] |
J. Humar and M. Ruban, Dynamics of Structures, CRC Press, Boca Raton, 2002. |
[10] |
A. E. Ingham, Some trigonometric inequalities in the theory of series, Mathem. Zeitschrift, 41 (1936), 367-379.
doi: 10.1007/BF01180426. |
[11] |
W. Littman and L. Markus, Stabilization of a hybrid system of elasticity by feedback boundary damping, Ann. Mat. Pura & Appl., 152 (1988), 281-330.
doi: 10.1007/BF01766154. |
[12] |
W. Littman and L. Markus, Exact boundary controllability of a hybrid system of elasticity, Arch. Rat. Mech. & Anal., 103 (1988), 193-236.
doi: 10.1007/BF00251758. |
[13] |
Ö. Morgül, B. P. Rao and F. Conrad, On the stabilization of a cable with a tip mass, IEEE Trans. Automat. Control, 39 (1994), 2140-2145.
doi: 10.1109/9.328811. |
[14] |
B. P. Rao, Uniform stabilization of a hybrid system of elasticity, SIAM J. Control. & Opt., 33 (1995), 440-454.
doi: 10.1137/S0363012992239879. |
[15] |
D. L. Russell, Nonharmonic Fourier Series in the Control Theory of Distributed Parameter Systems, J. Math. Anal. & Appl., 18 (1967), 542-560.
doi: 10.1016/0022-247X(67)90045-5. |
[16] |
N. Yebari and M. D. Aouragh, Uniform stabilization of a hybrid system of elasticity with variable coefficients, Int. J. Tomogr. & Stat., 10 (2008), 125-140. |
show all references
References:
[1] |
M. D. Aouragh and N. Yebari, Riesz basis approach and exponential stabilization of a nonhomogeneous flexible beam with a tip mass, Int. J. Math. & Stat., 7 (2010), 46-53. |
[2] |
S. Avdonin and S. Ivanov, Families of Exponentials: The Method of Moments in Controllability Problems for Distributed Parameter Systems, Cambridge University Press, Cambridge, New York, Melbourne, 1995. |
[3] |
M. S. Azam, N. Singh, A. Iyer and Y. P. Kakad, Detumbling and reorientation maneuvers and stabilization of NASA SCOLE system, IEEE Trans. Aerosp. & Electr. Syst., 28 (1992), 80-91.
doi: 10.1109/7.135434. |
[4] |
C. Baiocchi, V. Komornik and P. Loreti, Théorèmes du type Ingham et application à la théorie du contrôle, C. R. Acad. Sci. Paris Sér. I, Math., 326 (1998), 453-458.
doi: 10.1016/S0764-4442(97)89791-1. |
[5] |
W. E. Boyce and G. H. Handelman, Vibrations of rotating beams with tip mass, Angew. Math. & Phys., 12 (1961), 369-392.
doi: 10.1007/BF01600687. |
[6] |
F. Conrad and Ö. Morgül, On the stabilization of a flexible beam with a tip mass, SIAM J. Control. & Opt., 36 (1998), 1962-1986.
doi: 10.1137/S0363012996302366. |
[7] |
M. Grobbelaar-Van Dalsen, Uniform stability for the Timoshenko beam with tip load, J. Math. Anal. & and Appl., 361 (2010), 392-400.
doi: 10.1016/j.jmaa.2009.06.059. |
[8] |
B.-Z. Guo, Riesz basis approach to the stabilization of a flexible beam with a tip mass, SIAM J. Control. & Opt., 39 (2001), 1736-1747.
doi: 10.1137/S0363012999354880. |
[9] |
J. Humar and M. Ruban, Dynamics of Structures, CRC Press, Boca Raton, 2002. |
[10] |
A. E. Ingham, Some trigonometric inequalities in the theory of series, Mathem. Zeitschrift, 41 (1936), 367-379.
doi: 10.1007/BF01180426. |
[11] |
W. Littman and L. Markus, Stabilization of a hybrid system of elasticity by feedback boundary damping, Ann. Mat. Pura & Appl., 152 (1988), 281-330.
doi: 10.1007/BF01766154. |
[12] |
W. Littman and L. Markus, Exact boundary controllability of a hybrid system of elasticity, Arch. Rat. Mech. & Anal., 103 (1988), 193-236.
doi: 10.1007/BF00251758. |
[13] |
Ö. Morgül, B. P. Rao and F. Conrad, On the stabilization of a cable with a tip mass, IEEE Trans. Automat. Control, 39 (1994), 2140-2145.
doi: 10.1109/9.328811. |
[14] |
B. P. Rao, Uniform stabilization of a hybrid system of elasticity, SIAM J. Control. & Opt., 33 (1995), 440-454.
doi: 10.1137/S0363012992239879. |
[15] |
D. L. Russell, Nonharmonic Fourier Series in the Control Theory of Distributed Parameter Systems, J. Math. Anal. & Appl., 18 (1967), 542-560.
doi: 10.1016/0022-247X(67)90045-5. |
[16] |
N. Yebari and M. D. Aouragh, Uniform stabilization of a hybrid system of elasticity with variable coefficients, Int. J. Tomogr. & Stat., 10 (2008), 125-140. |
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