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Tytuł artykułu

Positivity and asymptotic stability of descriptor linear systems with regular pencils

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Języki publikacji
EN
Abstrakty
EN
The positivity and asymptotic stability of the descriptor linear continuous-time and discrete-time systems with regular pencils are addressed. Necessary and sufficient conditions for the positivity and asymptotic stability of the systems are established using the Drazin inverse matrix approach. Effectiveness of the conditions are demonstrated on numerical examples.
Słowa kluczowe
Rocznik
Strony
193--205
Opis fizyczny
Bibliogr. 23 poz., wzory
Twórcy
autor
  • The Author is with Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Bialystok
Bibliografia
  • [1] R. Bru, C. Coll, S. Romero-Vivo and E. Sanchez: Some problems about structural properties of positive descriptor systems. Positive systems (Rome, 2003), Lecture Notes in Control and Inform. Sci., bf 294 Springer, Berlin, 2003, 233-240.
  • [2] R. Bru, C. Coll and E. Sanchez: About positively discrete-time singular systems. In N.E. Mastorakis (Ed.) System and Control: theory and applications. Electrical and Computer Engineering Series,World Scientific and Engineering Society, Athens, 2000, 44-48.
  • [3] R. Bru, C. Coll and E. Sanchez: Structural properties of positive linear time-invariant difference-algebraic equations. Linear Algebra and its Applications, 349(1-3) (2002), 1-10.
  • [4] S. L. Campbell, C. D. Meyer and N. J. Rose: Applications of the Drazin inverse tolinear systems of differential equations with singular constructions. SIAM Journal on Applied Mathematics, 31(3), (1976), 411-425.
  • [5] C. Commalut and N. Marchand, EDS.: Positive systems. Lecture Notes in Control and Inform. Sci., 341 Springer-Verlag, Berlin, 2006.
  • [6] L. Dai: Singular control systems. Lectures Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1989.
  • [7] M. Dodig and M. Stosic: Singular systems state feedbacks problems. Linear Algebra and its Applications, 431(8), (2009), 1267-1292.
  • [8] M. H. Fahmy and J. O’Reill: Matrix pencil of closed-loop descriptor systems: infinite-eigenvalues assignment. Int. J. Control, 49(4), (1989), 1421-1431.
  • [9] L. Farina and S. Rinaldi: Positive Linear Systems. J. Willey, New York, 2000.
  • [10] F. R. Gantmacher: The theory of Matrices. Chelsea Publishing Co., New York, 1960.
  • [11] T. Kaczorek: Checking of the positivity of descriptor linear systems with singular pencils. Archives of Control Sciences, 22(1), (2012), 5-14.
  • [12] T. Kaczorek: Infinite eigenvalue assignment by output-feedbacks for singular systems. Int. J. of Applied Mathematics and Computer Science, 14(1), (2004), 19-23.
  • [13] T. Kaczorek: Linear Control Systems. 1 Research Studies Press J. Wiley, New York, 1992.
  • [14] T. Kaczorek: Polynomial and Rational Matrices. Applications in Dynamical Systems Theory. Springer-Verlag, London, 2007.
  • [15] T. Kaczorek: Positive 1D and 2D Systems. Springer-Verlag, London, 2002.
  • [16] T. Kaczorek : Positive linear systems with different fractional orders. Bulletin of the Polish Academy of Sciences: Technical Sciences, 58(3), (2010), 453-458.
  • [17] T. Kaczorek: Positivity of descriptor linear systems with regular pencils. Archives of Electrical Engineering, 61(1), (2012), 101-113.
  • [18] T. Kaczorek: Realization problem for singular positive continuous-time systems with delays. Control and Cybernetics, 36(1), (2007), 47-57.
  • [19] T. Kaczorek: Selected Problems of Fractional Systems Theory. Springer-Verlag, Berlin, 2011.
  • [20] T. Kaczorek: Stability of descriptor positive linear systems. COMPEL, 33(3), (2014), 1-14.
  • [21] V. Kucera and P. Zagalak: Fundamental theorem of state feedback for singular systems. Automatica, 24(5), (1988), 653-658.
  • [22] P. Van Dooren: The computation of Kronecker’s canonical form of a singular pencil. Linear Algebra and its Applications, 27 (1979), 103-140.
  • [23] E. Virnik: Stability analysis of positive descriptor systems, Linear Algebra and its Applications, 429 (2008), 2640-2659.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-76b7c912-2a33-413e-b89c-e0c42574929f
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