Externally and internally positive singular discrete-time linear systems

• Autorzy: Tadeusz Kaczorek
• Języki publikacji: EN

Abstrakty

EN

Notions of externally and internally positive singular discrete-time linear systems are introduced. It is shown that a singular discrete-time linear system is externally positive if and only if its impulse response matrix is non-negative. Sufficient conditions are established under which a single-output singular discrete-time system with matrices in canonical forms is internally positive. It is shown that if a singular system is weakly positive (all matrices E, A, B, C are non-negative), then it is not internally positive.

Słowa kluczowe

EN

singular; positive; internally; externally; system; linear

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2002
• Tom: 12
• Numer: 2
• Strony: 197-202

Daty

wydano

2002

otrzymano

2001-10-02

Twórcy

autor

Tadeusz Kaczorek

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

Bibliografia

• Cobb D. (1984): Controllability, observability and duality in singular systems. - IEEE Trans. Automat. Contr., Vol. AC-29, No. 12, pp. 1076-1082.
• Dai L. (1989): Singular Control Systems. - Berlin: Springer.
• Fanti M.P., Maione B. and Turchiano B. (1990): Controllability of multi-input positive discrete-time systems. - Int. J. Contr., Vol. 51, No. 6, pp. 1295-1308.
• Kaczorek T. (1993): Linear Control Systems, Vol. 2. - New York: Wiley.
• Kaczorek T. (1997): Positive singular discrete linear systems.-Bull. Pol. Acad. Techn. Sci., Vol. 45, No. 4, pp. 619-631.
• Kaczorek T. (1998a): Positive descriptor discrete-time linear systems. - Probl. Nonlin. Anal. Eng. Syst., Vol. 7, No. 1, pp. 38-54.
• Kaczorek T. (1998b): Weakly positive continuous-time linear systems. - Bull. Pol. Acad. Techn. Sci., Vol. 46, No. 2, pp. 233-245.
• Klamka J. (1991): Controllability of Dynamical Systems. - Dordecht: Kluwer.
• Lewis F.L. (1984): Descriptor systems: Decomposition into forward and backward subsystems. - IEEE Trans. Automat. Contr., Vol. AC-29, pp. 167-170.
• Lewis F.L. (1986): A survey of linear singular systems. - Circuits Syst. Signal Process., Vol. 5, No. 1, pp. 1-36.
• Luenberger G. (1977): Dynamic equations in descriptor form. - IEEE Trans. Automat. Contr., Vol. AC-22, No. 3, pp. 312-321.
• Luenberger D.G. (1978): Time-invariant descriptor systems. - Automatica, Vol. 14, No.2, pp. 473-480.
• Mertzios B.G. and Lewis F.L. (1989): Fundamental matrix of discrete singular systems.-Circuits Syst. Signal Process., Vol. 8, No. 3, pp. 341-355.
• 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.