On stability in impulsive dynamical systems

• Autorzy: Ciesielski K.
• Języki publikacji: EN

Abstrakty

EN

Several results on stability in impulsive dynamical systems are proved. The first main result gives equivalent conditions for stability of a compact set. In particular, a generalization of Ura's theorem to the case of impulsive systems is shown. The second main theorem says that under some additional assumptions every component of a stable set is stable. Also, several examples indicating possible complicated phenomena in impulsive systems are presented.

Słowa kluczowe

EN

dynamical system; flow; impulse; stability; invariance; prolongation

PL

układ dynamiczny; przepływ; impuls; stabilność; niezmienniczość; przedłużenie

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 1
• Strony: 81--91
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Ciesielski K.

• Mathematics Institute Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

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• [BS] N. P. Bhatia and G. P. Szegő, Stability Theory of Dynamical Systems, Springer, 2002.
• [C1] K. Ciesielski, Sections in semidynamical systems, Bull. Polish Acad. Sci. Math. 40 (1992), 297-307.
• [C2] -, On semicontinuity in impulsive dynamical systems, this volume, 71-80.
• [K1] S. Kaul, On impulsive semidynamical systems, J. Math. Anal. Appl. 150 (1990), 120-128.
• [K2] -, On impulsive semidynamical systems II, Recursive properties, Nonlinear Anal. 16 (1991), 635-645.
• [LBS] V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of Impulsive Differential Equations, World Sci., 1989.
• [NS] V. V. Nemytskiĭ and V. V. Stepanov, Qualitative Theory of Differential Equations, Princeton Univ. Press, 1960.
• [P] A. Pelczar, Introduction to the Theory of Differential Equations, Part II , Bibl. Mat. 67, Polish Sci. Publ., 1989 (in Polish).
• [V] J. de Vries, Elements of Topological Dynamics, Math. Appl. 257, Kluwer, 1993.