publication . Article . 2008

The motion planning problem and exponential stabilization of a heavy chain. Part II

Piotr Grabowski;
Open Access English
  • Published: 01 Jan 2008 Journal: Opuscula Mathematica (issn: 1232-9274, Copyright policy)
  • Publisher: AGH Univeristy of Science and Technology Press
Abstract
This is the second part of paper [P. Grabowski, The motion planning problem and exponential stabilization of a heavy chain. Part I, to appear in International Journal of Control], where a model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations was interpreted as an abstract semigroup system and then analysed on a Hilbert state space. In particular, in [P. Grabowski, The motion planning problem and exponential stabilization of a heavy chain. Part I, to appear in International Journal of Control] we have formulated the problem of exponential stabilizability of a heavy chain in a given position. It was...
Subjects
free text keywords: infinite-dimensional control systems, semigroups, motion planning problem, exponential stabilization, spectral methods, Riesz bases, exact observability, Applied mathematics. Quantitative methods, T57-57.97
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21 references, page 1 of 2

[1] W. Arendt, C.J.K. Batty, Tauberian theorems and stability of one-parameter semigroups, Transactions of the American Mathematical Society 306 (1988), 837-852. [OpenAIRE]

[2] A.V. Balakrishnan, Superstability of systems, Applied Mathematics and Computation 164 (2005), 321-326.

[3] S. Belyi, S. Hassi, H. de Snoo, E. Tsekanovskiˇi, A general realization theorem for matrix-valued Herglotz-Nevanlinna functions, Linear Algebra and Its Applications 419 (2006), 331-358. [OpenAIRE]

[4] R.F. Curtain, G. Weiss, Exponential stability of well-posed linear systems by colocated feedback. SIAM Journal on Control and Optimization 45 (2006), 273-297.

[7] I.C. Gohberg, M.G. Krein, Introduction to the Theory of Linear Non-selfadjoint Operators, Moscow: Nauka. 1965 (in Russian). English translation: Translations of Mathematical Monographs 18, Providence: AMS. 1969.

[8] P. Grabowski, The motion planning problem and exponential stabilization of a heavy chain. Part I, to appear in International Journal of Control.

[9] I.S. Gradshteyn, I.M. Ryzhik, Tables of integrals, series, and products, Academic Press, San Diego, CA, 1984. Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger. 6th ed.

[10] Haraux A., Une remarque sur la stabilisation de certains systèmes du deuxième ordre, Portugaliae Mathematica 46 (1989), 245-258. Scanned version available from The Portugal National Library URL: http://purl.pt/404/1/vol6-1947/jpg/spm_ 1989-fasc3_0019_245_t0.jpg

[11] A.E. Ingham, Some trigonometrical inequalities with applications to the theory of series, Mathematische Zeitschrift 41 (1936), 367-379. [OpenAIRE]

[12] V.E. Kacnel'son, Conditions under which systems of eigenvectors of some classes of operators form a basis, Funktsjonal'nyj Analiz i evo Prilozhenija 1 (1967), 39-51. English translation in: Functional Analysis and Its Applications 1 (1968), 122-132.

[13] J. Krzyż, Problems in Complex Variable Theory, Elsevier, New York, 1972.

[14] I. Lasiecka, R. Triggiani, L2(Σ) -regularity of the boundary to boundary operator B∗ L for hyperbolic and Petrowski PDEs, Abstract and Applied Analysis (2003), 19, 1061-1139 with complement: Lasiecka I., Triggiani R., The operator B∗ L for the wave equation with Dirichlet control, Abstract and Applied Analysis (2004) 7, 625-634. [OpenAIRE]

[15] Yu.I. Lyubich, Vu Quôc Phóng, Asymptotic stability of linear differential equations in Banach spaces, Studia Mathematica 88 (1988), 37-42. [OpenAIRE]

[16] J. Prüss, On the spectrum of C0-semigroup, TRANSACTIONS of the AMS 284 (1984), 847-857. [OpenAIRE]

[17] H. Röh, Spectral Analysis of Non Self-Adjoint C0-Semigroup Generators, PhD. Thesis. Department of Mathematics, Hariot-Watt University, February 1982.

21 references, page 1 of 2
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