Observability of small solutions of linear differential-algebraic systems with delays

• Autorzy: Zaczkiewicz Z. , Marchenko V.
• Języki publikacji: EN

Abstrakty

EN

In this paper we investigate observability of small solutions of linear differential-algebraic systems with delays (DAD), i.e. solutions that vanish after some finite time. In particular, we prove existence of two kinds of small solutions of DAD systems. The main result are the rank type conditions for observability of three kinds of small solutions of linear differential-algebraic systems with delay.

Słowa kluczowe

EN

observability; small solutions; differential-algebraic systems; time-delay

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2006
• Tom: Vol. 35, no 4
• Strony: 997--1013
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Zaczkiewicz Z.

autor

Marchenko V.

• Technical University of Bialystok, Institute of Mathematics & Physics, Wiejska 45a, 15-351 Białystok, Poland,

Bibliografia

• BOAS, R. (1954) Entire Functions. Academic Press, New York.
• GROSSMAN, R.L., NERODE, A., RAVN, A.P. et al. (1993) Hybrid Systems. Lecture Notes in Computer Science 736, Springer-Verlag, New York.
• HALE, J. H. and VERDUYN LUNEL, S. M. (1993) Introduction to Functional Differential Equations. Springer-Verlag, New York.
• HENRY, D. (1970) Small Solutions of Linear Autonomous Functional Differential Equations. J. Differential Equations 8, 494-501.
• KAPPEL, F. (1976) Laplace transform methods and linear autonomous functional differential equations. Math. Institut, Univ. Graz, Bericht 64.
• MANITIUS, A. (1982) F-controlability and observability of linear retarded systems. Appl. Math. Optim. 9, 73-95.
• MARCHENKO, V. M. and PODDUBNAYA, O. N. (2002) Representations of solutions for controlled hybrid systems. Problems of Control and Informatics (Kiev) 6, 17-25. (English translation: Journal of Automation and Information Sciences 34, 11-19).
• MARCHENKO, V.M., PODDUBNAYA, O.N. and ZACZKIEWICZ, Z. (2006) On the observability of linear differential-algebraic systems with delays. IEEE Trans. Automat. Contr. 51, 1387-1392.
• MARCHENKO, V.M. and ZACZKIEWICZ, Z. (2005) Observability for linear differential-algebraic systems with delays. In: Proc. IEEE Met. and Mod. Autom. Rob. (MMAR ), Miedzyzdroje, Poland, Aug./Sept 2005, 299-272.
• DE LA SEN, M. (1996) The reachability and observability of hybrid mulitrate sampling linear systems. Computer Math. Applic. 3(1), 109-122.
• VERDUYN LUNEL, S.M. (1986) A Sharp Version of Henry’s Theorem on Small Solutions. J. Differential Equations 62(2), 266-274.
• SALOMON, D. (1984) On controllability and observability of time delay systems. IEEE Trans. Automat. Contr. 29, 432-439.