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Computer aided methods for stability analysis of 2D linear systems described by the first Fornasini-Marchesini model

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Computer aided methods for investigation of the asymptotic stability of 2D discrete linear systems described by the first Fornasini-Marchesini model are given. The methods require computation of eigenvalues of complex matrices or values of complex functions. Effectiveness of the stability tests are demonstrated on numerical examples.
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Twórcy
autor
  • Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland
  • Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland, www: pb.edu.pl
Bibliografia
  • [1] Y. Bistritz, “On an inviable approach for derivation of 2-D stability tests”, IEEE Trans. Circuit Syst. II, vol. 52, no. 11, 2005, pp. 713–718. DOI:http://dx.doi.org/10.1109/TCSII.2005.852929
  • [2] M. Buslowicz, “Computer methods for stability investigation of the Fornasini-Marchesini model of linear 2D systems”, Measurement Automation and Robotics, no. 2, 2011, pp. 556–565 (in CD-ROM) (in Polish).
  • [3] M. Buslowicz, “Computational methods for investigation of stability of models of 2D continuousdiscrete linear systems”, Journal of Automation, Mobile Robotics & Intelligent Systems, vol. 5, no. 1, 2011, pp. 3–7.
  • [4] M. Buslowicz, “Stability of the second Fornasini-Marchesini type model of continuous-discrete linear systems”, Acta Mechanica et Automatica, vol. 5, no. 4, pp. 1–5, 2011.
  • [5] M. Buslowicz, A. Ruszewski, “Stability investigation of continuous-discrete linear systems”, Measurement Automation and Robotics, no. 2, 2011, pp. 566–575 (in CD-ROM) (in Polish).
  • [6] M. Buslowicz, A. Ruszewski, “Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems”, Int. J. Appl. Math. Comput. Sci., vol. 22, no. 2, 2012, pp. 401–408. DOI: http://dx.doi.org/10.2478/v10006-012-0030-9
  • [7] M. Buslowicz, A.E. Rzepecki, “Computer methods for stability investigation of the Roesser model of 2D linear systems”, Measurement Automation and Robotics, no. 2, 2012, pp. 298–302 (in CD-ROM) (in Polish).
  • [8] Y. Ebihara, Y. Ito, T. Hagiwara, “Exact stability analysis of 2-D systems using LMIs”, IEEE Trans. Automat. Control, vol.51, no. 9, 2006, pp. 1509–1513. DOI: http://dx.doi.org/10.1109/TAC.2006.880789
  • [9] E. Fornasini, G. Marchesini, “State-space realization theory of two-dimensional filters”, IEEE Trans. Automat. Control,vol. AC-21, 1976, pp. 484–492. DOI: http://dx.doi.org/10.1109/TAC.1976.1101305
  • [10] G.D. Hu, M. Liu, “Simple criteria for stability of two-dimensional linear systems”, IEEE Trans. Signal Processing, vol. 53, 2005, pp. 4720–4723.
  • [11] T. Kaczorek, Two-Dimensional Linear Systems, Springer, Berlin, 1985. DOI:http://dx.doi.org/10.1007/BFb0005617
  • [12] T. Kaczorek, Positive 1D and 2D Systems, Springer, London, 2002. DOI:http://dx.doi.org/10.1007/978-1-4471-0221-2
  • [13] T. Kaczorek, “LMI approach to stability of 2D positive systems with delays”, Multidimensional Systems and Signal Processing, vol. 20, 2009, pp. 39–54.
  • [14] T. Kaczorek, “Asymptotic stability of positive fractional 2D linear systems”, Bull. Pol. Acad. Sci.,Tech. Sci.,vol. 57, no. 3, 2009, pp. 289–292. DOI:http://dx.doi.org/10.2478/v10175-010-0131-2
  • [15] T. Kaczorek, “Practical stability of positive fractional 2D linear systems”, Multidimensional Systems and Signal Processing, vol. 21, 2010, pp. 231–238. DOI:http://dx.doi.org/10.1007/s11045-009-0098-z
  • [16] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer, Berlin 2011. DOI: http://dx.doi.org/10.1007/978-3-642-20502-6
  • [17] H. Kar, V. Sigh, “Stability of 2-D systems described by the Fornasini-Marchesini first model”, IEEE Trans. Signal Processing, vol. 51, 2003, pp. 1675–1676. Doi: http://dx.doi.org/10.1109/TSP.2003.811237
  • [18] L.H. Keel, S.P. Bhattacharyya, “A generalization of Mikhailov’s criterion with applications”. In: Proc. of the American Control Conference, Chicago, USA, vol. 6, 2000, pp. 4311–4315. DOI: http://dx.doi.org/10.1109/ACC.2000.877035
  • [19] J. Kurek, “Stability of positive 2D systems described by the Roesser model”, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 4, 2002, pp. 531–533.
  • [20] T. Liu, “Stability analysis of linear 2-D systems”, Signal Processing, vol. 88, 2008, pp. 2078–2084. DOI: http://dx.doi.org/10.1016/j.sigpro.2008.02.007
  • [21] W.-S. Lu, “On a Lyapunov approach to stability analysis of 2-D digital filters”, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 45, 1994, pp. 665–669. DOI: http://dx.doi.org/10.1109/81.329727
  • [22] T. Ooba, “On stability analysis of 2-D systems based on 2-D Lyapunov matrix inequalities”, IEEE Trans. Circuit Syst. I, Fundam. Theory Appl., vol. 47, 2000, pp. 1263–1265.
  • [23] W. Paszke, E. Rogers, P. Rapisarda, K. Gałkowski, A. Kummert, “New frequency domain based stability tests for 2D linear systems”, Proc. of 17th Int. Conf. Methods and Models in Automation and Robotics, 2012 (CD-ROM). DOI: http://dx.doi.org/10.1109/MMAR.2012.6347922
  • [24] M. Twardy, “An LMI approach to checking stability of 2D positive systems”, Bull. Pol. Acad. Sci., Tech. Sci., vol. 55, no. 4, 2007, pp. 385–395.
  • [25] X. Xiao, R. Unbehauen, “New stability test algorithm for two-dimensional digital filters”, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 45, no. 7, 1998, pp. 739–741.
  • [26] S.-F. Yang, C. Hwang, “s”, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, no. 7, 2000, pp. 1120–1123.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9644a22a-4739-4c1a-a05c-034b65552c22
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