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Stabilization of discrete-time LTI positive systems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper mitigates the existing conditions reported in the previous literature for control design of discrete-time linear positive systems. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteing asymptotic stability of discrete-time positive system structures, new conditions are presented with which the state-feedback controllers and the system state observers can be designed. Associated solutions of the proposed design conditions are illustrated by numerical illustrative examples.
Rocznik
Strony
575--594
Opis fizyczny
Bibliogr. 28 poz., wykr., wzory
Twórcy
autor
  • Technical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Cybernetics and Artificial Intelligence, Letná 9, 042 00 Košice, Slovakia
autor
  • Technical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Cybernetics and Artificial Intelligence, Letná 9, 042 00 Košice, Slovakia
Bibliografia
  • [1] F. Cacace, L. Farina, R. Setola and A. Germani (Eds.): Positive Systems. Lecture Notes in Control and Information Sciences LNCIS, 471 Springer, Cham, 2016.
  • [2] J. M. Carnicer, J. M. Pena and R. A. Zalik: Strictly totally positive systems. J. Approximation Theory, 92 (1998), 411-441.
  • [3] T. Kaczorek: Positive 1D and 2D Systems. Springer-Verlag, London, 2002.
  • [4] T. Kaczorek and L. Sajewski: The Realization Problem for Positive and Fractional Systems. Springer, Cham, 2014.
  • [5] Z. Shu, J. Lam, H. Gao, B. Du and L. Wu: Positive observers and dynamic output-feedback controllers for interval positive linear systems. IEEE Tran. Circuits and Systems, 55(10), (2008), 3209-3222.
  • [6] N. K. Son and D. Hinrichsen: Robust stability of positive continuous time systems. Numerical Functional Analysis and Optimization, 17(5-6), (1996), 649-659.
  • [7] J. Back and A. Astolfi: Design of positive linear observers for positive linear systems via coordinate transformations and positive realizations. SIAM J. on Control and Optimization, 47(1), (2008), 345-373.
  • [8] O. Pastravanu and M. H. Matcovschi: (M,β)-stability of positive linear systems. Mathematical Problems in Engineering, Article ID 9605464, 11p, (2016).
  • [9] T. Kaczorek: Positive stable realizations with system Metzler matrices. Archives of Control Sciences, 21(2), (2011), 122-142.
  • [10] B. Canto, R. Canto and S. Kostova: Stabilization of positive linear discrete-time systems by using a Brauers theorem. Scientific World Journal, Article ID 856356, 6p, (2014).
  • [11] T. Kaczorek: Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems. Archives of Control Sciences, 22(4), (2012), 451-465.
  • [12] X. Xue and L. Guo: A kind of nonnegative matrices and its application on the stability of discrete dynamical systems. J. Mathematical Analysis and Application, 331(2), (2007), 1113-1121.
  • [13] H. Gao, J. Lam, C. Wang and S. Xu: Control for stability and positivity. Equivalent conditions and computation. IEEE Trans. Automatic Control, 52(9), (2005), 540-544.
  • [14] M. Ait Rami and F. Tadeo: Controller synthesis for positive linear systems with bounded controls. IEEE Trans. Circuits and Systems, 54(2), (2007), 151-155.
  • [15] A. Berman, M. Neumann and R. Stern: Nonnegative Matrices in Dynamic Systems. John Wiley & Sons, New York, 1989.
  • [16] D. G. Luenberger: Introduction to Dynamic Systems. Theory, Models and Applications. John Wiley & Sons, New York, 1979.
  • [17] M. Ait Rami and F. Tadeo: Positive observation problem for linear discrete positive systems. Proc. 45th IEEE Conf. on Decision & Control, San Diego, CA, USA, (2006), 4729-4733.
  • [18] B. Shafai and A. Oghbaee: Positive quadratic stabilization of uncertain linear system. Proc. 2014 IEEE Multi-conference on Systems and Control, Antibes, France, (2014), 1412-1417.
  • [19] C. L. Philips and H.T. Nagle: Digital Control System Analysis and Design. Prentice Hall, Englewood Cliffs, 1984.
  • [20] P. De Leenheer and D. Aeyels: Stabilization of positive linear systems. Systems & Control Letters, 44(4), (2001), 259-271.
  • [21] L. Farina and S. Rinaldi: Positive Linear Systems. Theory and Applications. John Wiley & Sons, New York, 2000.
  • [22] C. A. R. Crusius and A. Trofino: Sufficient LMI conditions for output feedback control problems. IEEE Trans. Automatic Control, 44(5), (1999), 1053-1057.
  • [23] A. Filasová, D. Gontkovič and D. Krokavec: Observer-based fault estimation for linear systems with distributed time delay. Archives of Control Sciences, 23(2), (2013), 169-186.
  • [24] G. Birkhoff and S. Mac Lane: A survey of Modern Algebra. Macmillan Publishing, New York, 1977.
  • [25] D. J. S. Robinson: An Introduction to Abstract Algebra. Walter de Gruyter, Berlin, 2003.
  • [26] R. A. Horn and C. R. Johnson: Matrix Analysis. Cambridge University Press, New York, 2013.
  • [27] W. M. Haddad and V. Chellaboina: Nonlinear Dynamical Systems and Control. A Lyapunov-Based Approach. Princeton Univiversity Press, Princeton, 2008.
  • [28] D. Peaucelle, D. Henrion, Y. Labit and K. Taitz: User’s Guide for SeDuMi Interface. LAAS-CNRS, Toulouse, 2002
Uwagi
EN
The work presented in this paper was supported by VEGA, the Grant Agency of the Ministry of Education and the Academy of Science of Slovak Republic, under Grant No. 1/0608/17. This support is very gratefully acknowledged.
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
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