Analysis of some dual properties in discrete dynamic systems

• Autorzy: Zhirabok A.
• Języki publikacji: EN

Abstrakty

EN

The problem of duality in nonlinear and linear systems is considered. In addition to the known duality between controllability and observability, new dual notions and their properties are investigated. A way to refine these properties through an isomorphic transformation of the original systems is suggested.

Słowa kluczowe

EN

nonlinear system; linear system; algebraic approach; error correction; reachability; duality

PL

układ liniowy; układ nieliniowy; system dynamiczny; system dyskretny; dwoistość

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2006
• Tom: Vol. 16, no 3
• Strony: 297--308
• Opis fizyczny: Bibliogr. 14 poz., rys., tab.

Twórcy

autor

Zhirabok A.

• Far Eastern State Technical University 10 Pushkinskaya Str., Vladivostok, 690950, Russia,

Bibliografia

• [1] Arbib M. and Manes E. (1974): Foundation of system theory: Decomposable systems. - Automatica, Vol. 10, No. 2, pp. 285-302.
• [2] Bellman R. (1960): Introduction to Matrix Analysis. - New York: McGraw-Hill Company, Inc.
• [3] Gill A. (1971): Linear Sequential Circuits. Analysis, Synthesis, and Application. -New York: McGraw-Hill.
• [4] Goldblad R. (1979): Topoi. The Categorical Analysis of Logic. -Amsterdam: North-Holland.
• [5] Hermann R. and Krener A. (1977): Nonlinear controllability and observability. - IEEE Trans. Automat. Contr., Vol. AC-22, No. 5, pp. 728-740.
• [6] Korn G.A. and Korn T.M. (1961): Mathematical Handbook. - New York: McGraw-Hill.
• [7] Lankaster P. (1969): Theory of Matrices. -London: Academic Press.
• [8] Kwakernaak H. and Sivan R. (1972): Linear Optimal Control Systems. -New York: Wiley.
• [9] Michtchenko A. and Zhirabok A. (2001): Application of invariance for error correction in nonlinear systems. - Proc. 12-th Int. Symp. Danube Adria Association for Automation and Manufacturing, Vienna, Austria, pp. 297-298.
• [10] Peterson W. and Weldon E. (1972): Error-Correcting Codes. -London: Mita Press.
• [11] Shumsky A. and Zhirabok A. (2005): Nonlinear diagnostic filter design: Algebraic and geometric points of view. - Proc. 16-th IFAC World Congress, Prague, Czech Republic, (on CD-ROM).
• [12] Zhirabok A. and Shumsky A. (1993): A new mathematical technique for nonlinear systems research. - Proc. 12-th IFAC World Congress, Sydney, Australia, Vol. 3, pp. 485-488.
• [13] Zhirabok A. (1998): Observability and controllability properties of nonlinear dynamic systems.-Int. J. Comput. Syst. Sci., Vol. 37, No. 1, pp. 1-4.
• [14] Zhirabok A. (2000): On canonical decomposition of nonlinear dynamic systems, In: Nonlinear Control in the Year 2000, Vol. 2, (F. Lamnabhi-Lagarrigue, A. Isidori, W. Respondek, Eds.).-London: Springer, pp. 555-564.