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Controlling a non-homogeneous Timoshenko beam with the aid of the torque

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Języki publikacji
EN
Abstrakty
EN
Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they have finally the appropriate form and the results on C0-continuous semigroups may be applied.
Rocznik
Strony
587--598
Opis fizyczny
Bibliogr. 16 poz., rys.
Twórcy
autor
  • Institute of Mathematics, Szczecin University, ul. Wielkopolska 15, 70-451 Szczecin, Poland, sklar@univ.szczecin.pl
autor
Bibliografia
  • [1] Avdonin, S.A. and Ivanov, S.A. (1995). Families of Exponentials, Cambridge University Press, Cambridge.
  • [2] Avdonin, S. and Moran, W. (2001). Ingham-type inequalities and Riesz bases of divided differences, International Journal of Applied Mathematics Computer Science 11(4): 803–820.
  • [3] Kaczorek, T. (2012). Existence and determination of the set of Metzler matrices for given stable polynomials, International Journal of Applied Mathematics Computer Science 22(2): 389–399, DOI: 10.2478/v10006-012-0029-2.
  • [4] Kato, T. (1966). Perturbation Theory for Linear Operators, Springer-Verlag, Berlin.
  • [5] Krabs,W. and Sklyar, G.M. (2002). On Controllability of Linear Vibrations, Nova Science Publishers Inc., Huntington, NY.
  • [6] Levin, B. (1961). On Riesz bases of exponential in 12, Zapiski Matematicheskogo Otdieleniya Fiziko-matematicheskogo Fakul’teta Kharkovskogo Universiteta 27(4): 39–48.
  • [7] Ostalczyk, P. (2012). Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains, International Journal of Applied Mathematics Computer Science 22(3): 533–538, DOI: 10.2478/v10006-012-0040-7.
  • [8] Paley, R.E.A.C. and Wiener, N. (1934). Fourier Transforms in the Complex Domain, American Mathematical Society, Providence, RI.
  • [9] Respondek, J.S. (2008). Approximate controllability of infinite dimensional systems of the n-th order, International Journal of Applied Mathematics Computer Science 18(2): 199–212, DOI: 10.2478/v10006-008-0018-7.
  • [10] Russell, D.L. (1967). Non-harmonic Fourier series in control theory of distributed parameter system, Journal of Mathematical Analysis and Applications (18): 542–560.
  • [11] Sklyar, G.M. and Rezounenko, A.V. (2003). Strong asymptotic stability and constructing of stabilizing control, Matematitcheskaja Fizika, Analiz i Geometria 10(4): 569–582.
  • [12] Sklyar, G.M. and Szkibiel, G. (2007). Spectral properties of non-homogeneous Timoshenko beam and its controllability, Mekhanika Tverdogo Tela (37): 175–183.
  • [13] Sklyar, G.M. and Szkibiel, G. (2008a). Controllability from rest to arbitrary position of non-homogeneous Timoshenko beam, Matematitcheskij Analiz i Geometria 4(2): 305–318.
  • [14] Sklyar, G.M. and Szkibiel, G. (2008b). Spectral properties of non-homogeneous Timoshenko beam and its rest to rest controllability, Journal of Mathematical Analysis and Applications (338): 1054–1069.
  • [15] Sklyar, G.M. and Szkibiel, G. (2012). Approximation of extremal solution of non-Fourier moment problem and optimal control for non-homogeneous vibrating systems, Journal of Mathematical Analysis and Applications (387): 241–250.
  • [16] Zerrik, E., Larhrissi, R. and Bourray, H. (2007). An output controllability problem for semilinear distributed hyperbolic systems, International Journal of Applied Mathematics Computer Science 17(4): 437–448, DOI: 10.2478/v10006-007-0035-y.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-917953ca-80fa-4f90-ac84-d5c7efc21cf7
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