Locally positive nonlinear systems

• Autorzy: Tadeusz Kaczorek
• 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.

Słowa kluczowe

EN

local reachability in the direction of a cone; nonlinear system; time-varying; local positiveness

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: 13
• Numer: 4
• Strony: 505-509

Daty

wydano

2003

otrzymano

2003-05-25

poprawiono

2003-07-08

Twórcy

autor

Tadeusz Kaczorek

• Institute of Control and Industrial Electronics, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warszawa, Poland

Bibliografia

• 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.
• Berrman A., Neumann M. and Stern R. (1989): Nonnegative Matrices in Dynamic Systems. - New York: Wiley.
• Berman A. and Plemmons R.J. (1994): Nonnegative Matrices in Mathematical Sciences. - Philadelphia: SIAM Press.
• 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.
• 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.
• 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.
• Farina L. and Rinaldi S. (2000): Positive Linear Systems, Theory and Applications.- New York: Wiley.
• 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.
• Gantmacher F.R. (1959): The Theory of Matrices. - Chelsea, New York.
• Kaczorek T. (2001): Externally and internally positive time-varying linear systems. - Int. J. Appl. Math. Comput. Sci., Vol. 11, No. 4, pp. 957-964.
• Kaczorek T. (2002): Positive 1D and 2D Systems. -London: Springer-Verlag.
• Kaczorek T. (1998): Weakly positive continuous-time linear systems. - Bull. Pol. Acad. Sci. Techn. Sci., Vol. 46, No. 2, pp. 233-245.
• Kaczorek T. (1998): Positive descriptor discrete-time linear systems. - Probl. Nonlin. Anal. Eng. Syst., Vol. 1, No. 7, pp. 38-54.
• Klamka J. (1998): Constrained controllability of positive 2D systems. - Bull. Pol. Acad. Techn. Sci., Vol. 46, No. 1, pp. 93-102.
• 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.
• 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.
• Rumchev V.G. (2000): Feedback and positive feedback holdability of discrete-time systems. - Syst. Sci., Vol. 26, No. 3, pp. 15-23.
• 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.
• 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.
• 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.
• Walczak S. (1984): A note on the controllability of nonlinear systems. - Math. Syst. Theory, Vol. 17, pp. 351-356.
• Valcher M.E. (1996): Controllability and reachability criteria for discrete-time positive systems. - Int. J. Contr., Vol. 65, No. 3, pp. 511-536.
• 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.