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Locally Positive Nonlinear Systems

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Języki publikacji
EN
Abstrakty
EN
The notion of locally positive nonlinear time-varying linear systems is introduced. Necessary and sufficient conditions for the local positiveness of nonlinear time-varying systems are established. The concept of local reachability in the direction of a cone is introduced, and sufficient conditions for local reachability in the direction of a cone of this class of nonlinear systems are presented.
Twórcy
autor
  • Warsaw University of Technology Faculty of Electrical Engineering Institute of Control and Industrial Electronics 00-662 Warszawa, Koszykowa 75, Poland
Bibliografia
  • [1] d’Alessandro P. and de Santis E. (1994): Positivness of dynamic systems with non positive coefficients matrices. — IEEE Trans. Automat. Contr., Vol. AC-39, pp. 131–134.
  • [2] Berrman A., Neumann M. and Stern R. (1989): Nonnegative Matrices in Dynamic Systems.—New York: Wiley.
  • [3] Berman A. and Plemmons R.J. (1994): Nonnegative Matrices in Mathematical Sciences.—Philadelphia: SIAM Press.
  • [4] Caccetta L. and Rumchev V.G. (1998): Reachable discrete-time positive systems with minimal dimension control sets. — Dynam. Cont. Discr. Impuls. Syst., Vol. 4, pp. 539–552.
  • [5] Caccetta L. and Rumchev V.G. (2000): A survey of reachability and controllability for positive linear systems. — Ann. Opers. Res., Vol. 98, pp. 101–122.
  • [6] Fanti M.P., Maione B. and Turchsano B. (1990): Controllability of multi-input positive discrete-time systems. — Int. J. Contr., Vol. 51, No. 6, pp. 1295–1308.
  • [7] Farina L. and Rinaldi S. (2000): Positive Linear Systems, Theory and Applications.—New York: Wiley.
  • [8] Fornasini E. and Valcher M.E. (1997): Recent developments in 2D positive systems theory. — J. Appl. Math. Comp. Sci., Vol. 7, No. 4, pp. 713–735.
  • [9] Gantmacher F.R. (1959): The Theory of Matrices. — Chelsea, New York.
  • [10] Kaczorek T. (2001): Externally and internally positive time-varying linear systems. — Int. J. Appl. Math. Comput. Sci., Vol. 11, No. 4, pp. 957–964.
  • [11] Kaczorek T. (2002): Positive 1D and 2D Systems. — London: Springer-Verlag.
  • [12] Kaczorek T. (1998): Weakly positive continuous-time linear systems. — Bull. Pol. Acad. Sci. Techn. Sci., Vol. 46, No. 2, pp. 233–245.
  • [13] Kaczorek T. (1998): Positive descriptor discrete-time linear systems. — Probl. Nonlin. Anal. Eng. Syst., Vol. 1, No. 7, pp. 38–54.
  • [14] Klamka J. (1998): Constrained controllability of positive 2D systems. — Bull. Pol. Acad. Techn. Sci., Vol. 46, No. 1, pp. 93–102.
  • [15] Klamka J. and Kalinowski J. (1998): Reachability and controllability of positive continuous-time linear systems with time variable coefficients. — Bull. Pol. Acad. Techn. Sci., Vol. 49, No. 4, pp. 633–641.
  • [16] Ohta Y., Madea H. and Kodama S. (1984): Reachability, observability and realizability of continuous-time positive systems. — SIAM J. Contr. Optim., Vol. 22, No. 2, pp. 171–180.
  • [17] Rumchev V.G. (2000): Feedback and positive feedback holdability of discrete-time systems. — Syst. Sci., Vol. 26, No. 3, pp. 15–23.
  • [18] Rumchev V.G. and Anstee R.P. (1999): Asymptotic reachable sets for discrete-time positive linear systems.—Syst. Sci., Vol. 25, No. 1, pp. 41–47.
  • [19] Rumchev V.G. and James D.J.G. (1995): Spectral characterisation and pole assignment for positive linear discrete-time systems. — Int. J. Syst. Sci., Vol. 26, No. 2, pp. 295–312.
  • [20] Rumchev V.G. and James D.J.G. (1990): The role of nonnegative matrices in discrete-time mathematical modelling. — Int. J. Math. Educ. Sci. Technol., Vol. 21, No. 2, pp. 169–182.
  • [21] Walczak S. (1984): A note on the controllability of nonlinear systems.—Math. Syst. Theory, Vol. 17, pp. 351–356.
  • [22] Valcher M.E. (1996): Controllability and reachability criteria for discrete-time positive systems.—Int. J. Contr., Vol. 65, No. 3, pp. 511–536.
  • [23] Valcher M.E. (1997): On the internal stability and asymptotic behaviour of 2D positive systems. — IEEE Trans. Circ. Syst., Part I, Vol. 44, pp. 602–613.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0002-0045
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