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Tytuł artykułu

Robust stability of positive linear time delay systems under time-varying perturbations

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
By a novel approach, we get explicit robust stability bounds for positive linear time-invariant time delay differential systems subject to time-varying structured perturbations or non-linear time-varying perturbations. Some examples are given to illustrate the obtained results. To the best of our knowledge, the results of this paper are new.
Rocznik
Strony
947--954
Opis fizyczny
Bibliogr. 38 poz., rys.
Twórcy
  • Department of Mathematics, Vietnam National University-HCMC, International University, Thu Duc District, Saigon, Vietnam
autor
  • Department of Mathematics, Vietnam National University-HCMC, University of Information Technology, Thu Duc District, Saigon, Vietnam
Bibliografia
  • [1] J. Baranowski and W. Mitkowski, “Stabilisation of LC ladder network with the help of delayed output feedback”, Control and Cybernetics 41, 13-34 (2012).
  • [2] M. Buslowicz, “Robust stability of positive continuous-time linear systems with delays”, Int. J. Appl. Math. Comput. Sci. 20, 665-670 (2010).
  • [3] A.Berman and R.J. Plemmons, Nonnegative Matrices in Mathematical Sciences, Acad. Press, New York, 1979.
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  • [7] L. Farina and S. Rinaldi, Positive Linear Systems: Theory and Applications, John Wiley and Sons, New York, 2000.
  • [8] H. Górecki, S. Fuksa, P. Grabowski, and A. Korytowski, Analysis and Synthesis of Time-delay Systems, J. Wiley & PWN, Chichester & Warsaw, 1989.
  • [9] A. Goubet-Bartholome¨us, M. Dambrine, and J.P. Richard, “Stability of perturbed systems with time-varying delays”, Systems & Control Letters 31, 155-163 (1997).
  • [10] W.M. Haddad and V. Chellaboina, “Stability theory for nonnegative and compartmental dynamical systems with time delay”, Systems and Control Letters 51, 355-361 (2004).
  • [11] W.M. Haddad and V. Chellaboina, “Stability and dissipativity theory for nonnegative dynamical systems: a unified analysis framework for biological and physiological systems”, Nonlinear Anal. Real World Appl. 6, 35-65 (2005).
  • [12] W.M. Haddad, V. Chellaboina, and Q. Hui, Nonnegative and Compartmental Dynamical Systems, Princeton University Press, New York, 2010.
  • [13] J. Hale and S.M.V. Lunel, Introduction to Functional Differential Equations, Springer, New York, 1993.
  • [14] Q.L. Han, “Robust stability for a class of linear systems with time-varying delay and nonlinear perturbations”, Computers & Mathematics with Applications 47, 1201-1209 (2004).
  • [15] D. Hinrichsen and A.J. Pritchard, “ Stability radius for structured perturbations and the algebraic Riccati equation”, Systems & Control Letters 8, 105-113 (1986).
  • [16] D. Hinrichsen, A. Ilchmann, and A.J. Pritchard, “Robustness of stability of time-varying linear systems”, J. Differential Equations 82, 219-250 (1989).
  • [17] D. Hinrichsen and A.J. Pritchard, “Robust exponential stability of time-varying linear systems under time-varying parameter perturbations”, Int. J. Robust and Nonlinear Control 3, 63-83 (1993).
  • [18] D. Hinrichsen and A.J. Pritchard. Mathematical Systems Theory I, Springer, Berlin, 2005.
  • [19] G. Hu and E.J. Davison, “Real stability radii of linear timeinvariant time-delay systems”, Systems & Control Letters 50, 209-219 (2003).
  • [20] T. Kaczorek, “Stability of positive continuous-time linear systems with delays”, Bull. Pol. Ac.: Tech. 57, 395-398 (2009).
  • [21] J.H. Kim, “Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty”, IEEE Transactions on Automatic Control 46, 789-792 (2001).
  • [22] V.B. Kolmanovskii and V.R. Nosov, Stability of Functional Differential Equations, Academic Press, London, 1986.
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  • [27] W. Mitkowski, “Remarks on stability of positive linear systems”, Control and Cybernetics 29, 295-304 (2000).
  • [28] W. Mitkowski, “Dynamical properties of Metzler systems”, Bull. Pol. Ac.: Tech. 56, 309-312 (2008).
  • [29] P.H.A. Ngoc, “A Perron-Frobenius theorem for a class of positive quasi-polynomial matrices”, Applied Mathematics Letter 19, 747-751 (2006).
  • [30] P.H.A. Ngoc, T. Naito, and J.S. Shin, “Characterizations of positive linear functional differential equations”, Funkcialaj Ekvacioj 50, 1-17 (2007).
  • [31] P.H.A. Ngoc, “Stability radii of positive linear Volterra- Stieltjes equations”, J. Differential Equations 243, 101-122 (2007).
  • [32] P.H.A. Ngoc, “Strong stability radii of positive linear timedelay systems”, Int. J. Robust and Nonlinear Control 15, 459-472 (2005).
  • [33] P.H.A. Ngoc, “On positivity and stability of linear Volterra systems with delay”, SIAM J. on Control and Optimization 48, 1939-1960 (2009).
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  • [37] N.K. Son and P.H.A. Ngoc, “Robust stability of positive linear delay systems under affine parameter perturbations”, Acta Mathematica Vietnamica 24, 353-372 (1999).
  • [38] J.J. Yan, J.S.H. Tsai, and F.C. Kung, “A new result on the robust stability of uncertain systems with time-varying delay”, IEEE Trans. on Circuits and Systems I: Fundamental Theory and Applications 48, 914-916 (2001)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-992970c0-a7df-4dcf-be6d-fe3cbecf4803
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