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Positive fractional discrete-time Lyapunov systems

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Języki publikacji
EN
Abstrakty
EN
The positive linear fractional discrete-time Lyapunov systems are introduced. The necessary and sufficient conditions for the positivity, reachability, controllability to zero and observability of the systems are established. The sufficient conditions for stability are given. The notion of the dual positive fractional Lyapunov system is introduced and the relationship between the reachability and observability is given. The considerations are illustrated on the numerical example.
Rocznik
Strony
121--134
Opis fizyczny
Bibliogr. 47 poz., rys., tab., wzory
Twórcy
  • Warsaw University of Technology, Institute of Control and Industrial Electronics, Koszykowa 75, 00-662 Warsaw, Poland, przyborp@isep.pw.edu.pl
Bibliografia
  • [1] L. BENVENUTI and L. FARINA: A tutorial on positive realization problem. IEEE Trans. Autom. Control, 49(5), (2004), 651-664.
  • [2] M. BOLOGNA and P. GRIGOLINI: Physics of fractal operators. Springer-Verlag, New York, 2003.
  • [3] M. BUSŁOWICZ and T. KACZOREK: Reachability and minimum energy control of positive linear discrete-time systems with one delay. 12th Mediterranean Conf. Control and Automation, Kusadasi, Izmir, Turkey, (2004).
  • [4] A. DZIELINSKI and D. SIEROCIUK: Stability of discrete fractional order statespace systems. Proc. of 2nd IFAC Workshop on Fractional Differentiation and its Applications, (2006).
  • [5] L. FARINA and S. RINALDI: Positive linear systems; Theory and applications. J. Wiley, New York, 2000.
  • [6] N. M. F. FERREIRA and J.A. T. MACHADO: Fractional-order hybrid control of robotic manipulators. Proc. 11th Int. Conf. Advanced Robotics, Coimbra, Portugal, (2003), 393-398.
  • [7] K. GAŁKOWSKI: Fractional polynomials and nD systems. Proc. IEEE Mt. Symp. Circuits and Systems, Kobe, Japan, (2005), CD-ROM.
  • [8] T. KACZOREK: Positive 1D and 2D systems. Springer Verlag, London 2001.
  • [9] T. KACZOREK: Vectors and matrices in automation and electrotechnics. Wydawnictwo Naukowo-Techniczne, Warszawa, 1998, (in Polish).
  • [10] T. KACZOREK: New reachability and observability tests for positive linear discrete-time systems. Bull. Pol. Acad. Sci. Techn., 55(1), (2007).
  • [11] T. KACZOREK: Realization problem for positive discrete-time systems with delay. System Science, 30(4), (2004), 117-130.
  • [12] T. KACZOREK: Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs. Int. J. AppL Math. Comp. Sci., 16(2), (2006), 101-106.
  • [13] T. KACZOREK: A realization problem for positive continuous-time systems with reduced number of delays. Int. J. AppL Math. Comp. Sci., 16(3),(2006), 101-117.
  • [14] T. KACZOREK: Positive discrete-time linear Lyapunov systems. Proc. 15th Mediterranean Conf. Control and Automation, Athens, Greece, (2007).
  • [15] T. KACZOREK: Stability of positive discrete-time systems with time-delay. Proc. 8th World Multi-Conf. Systemics, Cybernetics and Informatics, Orlando, USA, (2004).
  • [16] T. KACZOREK: Reachability and controllability to zero of positive fractional discrete-time systems. Machine Intelligence and Robotic Control, 6(4), (2007).
  • [17] T. KACZOREK: Reachability and controllability to zero tests for standard and positive fractional discrete-time systems. J European System Engn., (2008), submitted.
  • [18] T. KACZOREK and M. BUSŁOWICZ: Minimal realization problem for positive multivariable linear systems with delay. Int. J. Appl. Math. Comp. Sci., 14(2), (2004), 181-187.
  • [19] T. KACZOREK and M. BUSŁOW1CZ: Recent developments in theory of positive discrete-time linear systems with delays - stability and robust stability. Pomiary, Automatyka, Kontrola, 9 (2004), 9-12.
  • [20] T. KACZOREK and M. BUSŁOWICZ: Recent developments in theory of positive discrete-time linear systems with delays - reachability, minimum energy control and realization problem. Pomiary, Automatyka, Kontrola, 9 (2004), 12-15.
  • [21] T. KACZOREK and P. PRZYBOROWSKI: Positive continues-time linear Lyapunov systems. Proc. Int. Conf Computer as a Tool, Warsaw, Poland, (2007), 731-737.
  • [22] T. KACZOREK and P. PRZYBOROWSKI: Positive continuous-time linear timevarying Lyapunov systems. Proc. XVI Int. Conf. Systems Science, 1 Wroclaw, Poland, (2007), 140-149.
  • [23] T. KACZOREK and P. PRZYBOROWSKI: Continuous-time linear Lyapunov conesystems. Proc. 13th IEEE IFAC Int. Conf. Methods and Models in Automation and Robotics, Szczecin, Poland, (2007), 225-229.
  • [24] T. KACZOREK and P. PRZYBOROWSKI: Positive linear Lyapunov systems. FNAANS Mt. J. - Problems of Nonlinear Analysis in Engineering Systems Journal, 13(2), (2007), 35-60.
  • [25] T. KACZOREK and P. PRZYBOROWSKI: Positive discrete-time linear Lyapunov systems with delays. Proc. Int. Workshop "Computational Problems of Electrical Engineering", (2007), Wilkasy, Poland, Electrical Review, 2k (2007), 12-15.
  • [26] J. KLAMKA: Controllability of dynamical systems, Kluwer Academic Publ. Dordrcht 1991.
  • [27] K. S. MILLER and B. Ross: An introduction to the fractional calculus and fractional differential equations. Willey, New York, 1993.
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  • [34] P. OSTALCZYK: Fractional-order backward difference equivalent forms. Part I -Horner's form. Proc. 1st IFAC Workshop Fractional Differentation and its Applications, Enseirb, Bordeaux, France, (2004), 342-347.
  • [35] P. OSTALCZYK: Fractional-order backward difference equivalent forms. Part II -Polynomial form. Proc. 1st IFAC Workshop Fractional Differentation and its Applications, Enseirb, Bordeaux, France, (2004), 348-353.
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  • [41] M. E. REYES-MELO, J. J. MARTINEZ-VEGA, C. A. GUERRERO-SALAZAR and U. ORTIZ-MENDEZ: Modelling and relaxation phenomena in organic dielectric materials. Application of differential and integral operators of fractional order. J. Optoel. Adv. Mat., 6(3), (2004), 1037-1043.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSW3-0045-0008
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