Externally and internally positive time-varying linear systems

• Autorzy: Tadeusz Kaczorek
• Języki publikacji: EN

Abstrakty

EN

The notions of externally and internally positive time-varying linear systems are introduced. Necessary and sufficient conditions for the external and internal positivities of time-varying linear systems are established. Moreover, sufficient conditions for the reachability of internally positive time-varying linear systems are presented.

Słowa kluczowe

EN

None

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2001
• Tom: 11
• Numer: 4
• Strony: 957-964

Daty

wydano

2001

otrzymano

2001-06-01

Twórcy

autor

Tadeusz Kaczorek

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

Bibliografia

• d'Alessandro P. and de Santis E. (1994): Positiveness 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.
• 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. App. Math. Comp. Sci., Vol.7, No.4, pp.101–123.
• Gantmacher F.R. (1959): The Theory of Matrices. — New York: Chelsea.
• Kaczorek T. (1998a): Weakly positive continuous-time linear systems. — Bull. Pol. Acad. Techn. Sci., Vol.46, No.2, pp.233–245.
• Kaczorek T. (1998b): Positive descriptor discrete-time linear systems. — Prob. Nonlin. Anal. Eng. Syst., Vol.1, No.7, pp.38–54.
• Kaczorek T. (2001): Positive 1D and 2D Systems. — London: Springer.
• Klamka J. (1998): Constrained controllability of positive 2D systems. — Bull. Pol. Acad. Techn. Sci., Vol.46, No.1, pp.93–102.
• 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.
• Ratajczak Z. (1967): On solutions of the system of homogenous differential linear equations. — Scientific Fasicicles of Poznań University of Technology, Mathematics, No.3 pp.59– 64 (in Polish).
• 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.
• 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.
• 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, Part I. — IEEE Trans. Circ. Syst., Vol.44, No.7, pp.602–613.