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Lagrange and practical stability criteria for dynamical systems with nonlinear perturbations

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Języki publikacji
EN
Abstrakty
EN
In the paper two classes of nonlinear dynamical system with perturbations are considered. The sufficient conditions for robust Lagrange and practical stability are proven with theorems, applying the theory of nonlinear operators of the functional analysis. The presented criteria give also the bounds of the analyzed dynamical processes. Three examples comparing the numerical computer solutions and the analytical investigation of the stability of the systems are given. The method can be applied to analytical and computer modeling of nonlinear dynamical systems, synthesis of computer control and optimization.
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43--58
Opis fizyczny
Bibliogr. 16 poz., rys., tab., wzory
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autor
Bibliografia
  • [1] A. V. Balakrishnan: Applied functional analysis. Springer-Verlag, 1976.
  • [2] Wu Hansheng and K. Mizukami: Robust stability criteria for dynamical systems including delayed perturbations. IEEE Trans. on Automatic Control, 40(3) (1995), 487-490.
  • [3] T. Kato: Perturbation theory for linear operators. Springer-Verlag, 1995.
  • [4] P. Kokotovic and R. Yackel: Singular perturbation of linear regulators: Basic theorems. IEEE Trans. on Automatic Control, 17(1), (1972), 29-37.
  • [5] G. Korn and T. Korn: Mathematical handbook. Mc-Graw-Hill Book Company, 1968.
  • [6] M. A. Krasnoselskii: Approximate solution of operator equations. Nauka, Moscow, 1969, (in Russian).
  • [7] A. Krumov: Perturbation method for modeling of nonlinear dynamical systems and robust sufficient conditions for its application. Proc. of IEEE Conf. EUROCON 2007 "Computer as a tool", Warsaw, Poland, (2007), 2298-2304.
  • [8] Cao Liyu, H.M Schwartz: Complementary results on the stability bounds of singularly perturbed systems. IEEE Trans. on Automatic Control, 49(11), (2004), 2017-2021.
  • [9] A. Nayfeh: Perturbation Methods. John Wiley Ltd., 2000.
  • [10] V. Trenoguine: Analyse fonctionelle. Nauka, Moscow, 1987, (in French).
  • [11] H. Trinh and M. Aldeen: On robustness and stabilization of linear systems with delayed nonlinear perturbations. IEEE Trans. on Automatic Control, 42(7), (1997), 1005-1007.
  • [12] Wikipedia on Answers.com: List of Banach spaces: http://www.answers.com/topic/list-of-banach-spaces
  • [13] Wanzhsu Ye and Xingwei Zhou: Criteria of convergence of median filters and perturbation theorem. IEEE Trans. on Signal Processing, 49(2), (2001), 360-363.
  • [14] G. Zames: Functional analysis applied to nonlinear feedback systems. IEEE Trans. on Circuit and Systems, CT-19 (1963), 392-404.
  • [15] G. Zeidler: Nonlinear functional analysis and its applications: Fixed point theorems. Springer-Verlag, 1985.
  • [16] Lei Zhou and Guoping Lu: Robust stability of singularly perturbed descriptor systems with nonlinear perturbation. IEEE Trans. on Automatic Control, 56(4), (2011), 858-863.
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Bibliografia
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bwmeta1.element.baztech-article-BSW3-0098-0004
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