Degenerate systems described by generalized invertible operators and controllability

• Autorzy: Thi H. V.
• Języki publikacji: EN

Abstrakty

EN

The theory of right invertible operators was started with works of D. Przeworska-Rolewicz and then it has been developed by M. Tasche, H. von Trotha, Z. Binderman and many other mathematicians (see [10]). Nguyen Dinh Quyet (in [5, 7]), has considered the controllability of linear system described by right invertible operators where the resolving operator is invertible. These results were generalized by A. Pogorzelec in the case of one-sized invertible resolving operator (see [9]) and by Nguyen Van Mau for the system described by generalized invertible operator (see [3]). However, for the degenerate systems, the problem has not been investigated. In this paper, we deal with the initial value problem for degenerate system of the form (2.7)-(2.8) and the controllability of this system.

Słowa kluczowe

EN

invertible operators; linear space; boundary value problem; degenerate systems

PL

przestrzeń linearna; zagadnienia brzegowe; operatory odwracalne; systemy zdegenerowane

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 2
• Strony: 419--430
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Thi H. V.

• Hong Duc University, Faculty of Natural Science, 307 - Le Lai Street, Thanh Hoa City, Vietnam

Bibliografia

• [1] Z. Binderman, Initial operators for generalized invertible operators, Comment. Math. XXXI (1991), 25-37.
• [2] Nguyen Van Mau, Controllability of general linear systems with right invertible operators, preprint No. 472, Institute of Mathematics, Polish Acad. Sci., Warszawa, 1990
• [3] Nguen Van Mau, Boundary value problems and controllability of linear systems with right invertible operators, Dissertationes Math., CCCXVI, Warszawa, 1992.
• [4] Nguyen Van Mau and Nguyen Minh Tuan, Algebraic properties of generalized right invertible operators, Demonstratio Math. XXX (3)(1997), 495-508.
• [5] Nguyen Dinh Quyet, Controllability and observability of linear systems described by the right invertible operators in linear space, Preprint No. 113, Institute of Mathematics, Polish Acad. Sci., Warszawa, 1977.
• [6] Nguyen Dinh Quyet, On linear systems described by right invertible operators acting in a linear space, Control and Cybernetics 7, (1978), 33-45.
• [7] Nguyen Dinh Quyet, On the F1-controllability of the system described by the right invertible operators in linear spaces, Methods of Mathematical Programming, System Research Institute, Polish Acad. Sci., PWN-Polish Scientific Publisher, Warszawa 1981, 223-226.
• [8] Nguyen Dinh Quyet, Hoang Van Thi, The Controllability of Degenerate System Described by Right Invertible Operators, VNU. Journal of Science, Mathematics-Physics, Viet Nam National University, Ha Noi, T. XVIII, No 3 (2002), 37-48.
• [9] A. Pogorzelec, Solvability and controllability of ill-determined systems with right invertible operators, Ph.D. Diss., Institute of Mathematics, Technical University of Warsaw, Warszawa, 1983.
• [10] D. Przeworska-Rolewicz, Algebraic Analysis, PWN and Reidel, Warszawa-Dordrecht, 1988.
• [11] D. Przeworska-Rolewicz and S. Rolewicz, Equations in Linear Spaces, Monografie Math. 47, PWN, Warszawa, 1968.