Investigations of the properties motion for essential nonlinear systems perturbed by impulses on some hypersurfaces

Nonlinear Analysis, Theory, Methods and Applications

Volumn 62, Issue 2, 2005, Pages 345-363

  Borysenko, S D ^a   Iovane, G ^b   Giordano, P ^b  

^a NATIONAL TECHNICAL UNIVERSITY OF UKRAINE   (Ukraine)

^b UNIVERSITY OF SALERNO   (Italy)

Author keywords

Impulse perturbations; Practical stability; Stability

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; DIFFERENCE EQUATIONS; FUNCTIONS; INTEGRATION; MATRIX ALGEBRA; PERTURBATION TECHNIQUES;

CAUCHY MATRIX SYSTEM; EXPONENTIAL STABILITY; IMPULSE PERTURBATIONS; PRACTICAL STABILITY;

NONLINEAR SYSTEMS;

EID: 18944396632     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.03.031     Document Type: Article

References (39)

1. E.A. Barbashin On stability with respect to impulse excitations Differential Equations 2 7 1966 863 871
2. R. Bellman Theory of Solution Stability of Differential Equations 1954 Isdatelstvo Inostz. Lit Moscow
3. J. Bihari A generalization of lemma of Bellman and its application to uniqueness problems of differential equations Acta Math. Acad. Sci. Hungar. 7 1 1956 71 94
4. A. Blaquiere Differential games with piecewise continuous trajectories Lecture Notes in Control and Information Sciences vol. 3 1977 Springer Berlin 34 69
5. S.D. Borysenko Estimates technical stability on nonlinear approximation Mat. Fiz. 29 1981 12 18
6. S.D. Borysenko About asymptotical stability solutions systems with impulse influence Ukrain. Mat. Zh. 35 2 1983 144 150
7. S.D. Borysenko, On solution stability on linear approximation of the systems with impulse, Differential Equations 22 (5) (1986) 884-886.
8. S.D. Borysenko Integro-sum inequalities for functions of many independent variables Differential Equations 23 9 1989 1638 1641
9. S.D. Borysenko Construction of Mathematical Models 1995 Vipol Kiev
10. S.D. Borysenko On Integro-sum functional inequalities Differential Equations 34 6 1998 850
11. S.D. Borysenko Multidimensional integro-sum inequalities Ukrain. Mat. Zh. 50 2 1998 172 177
12. D.S. Borysenko, About one integral inequality for piece-wise continuous functions, Proceedings of the X International Kravchuk Conference, Kyiv, 2004, 323.
13. S.D. Borysenko, M. Ciarletta, G. Iovane, Integro-sum inequalities and motion stability of systems with impulse perturbations, Nonlinear Anal., Theory Methods Appl., 2005, in this issue.
14. S.D. Borysenko, V.I. Kosolapov, and A.V. Obolensky Stability of Process under Continuous and Discrete Disturbances 1988 Naukova Dumka Kiev
15. N.G. Chetaev Motion Stability 1946 Gostekhisdat Moscow, Leningrad
16. M. Ciarletta, S.D. Borysenko, G. Iovane, About stability systems with impulse influence on nonlinear approximation, Proceedings of the X International Kravchuk Conference, Kiev, 2004, pp. 275-276.
17. B.P. Demidovich About one generalization criterion Lyapunov's stability for regular systems Mat. Sb. 66 3 1965 344 353
18. B.P. Demidovich Lectures on Mathematical Stability Theory of Motion 1967 Nauka Moscow
19. N.N. Krylov, N.N. Bogolyubov, Introduction in Nonlinear Machanics, Izd. Acad. Sci. Ukr. SSR., Kiev, 1937.
20. V. Lakshmikantham, Trends in the theory of impulsive differential equations, Proceedings of the International Conference on the Theory and Applications of Differential Equations, Ohio University, 1988, pp. 76-87.
21. V. Lakshmikantham, and S. Leela Differential and Integral Inequalities, Theory and Applications 1969 Academic Press New York
22. A.M. Lyapunov General problem on motion stability Collection works., Moscow 2 1956 7 264
23. V.D. Milman, and A.D. Myshkis About stability of motion with pusches Sibirsk. Mat. Zh. 1 2 1960 233 237
24. Yu.A. Mitropolsky, S. Leela, and A. Martynyuk About some directions of investigations of V. Lakshmikantham in the theory of differential equations and applications Differentsial'nye Uravneniya 22 4 1986 55 572
25. N.D. Moiseev, On some methods of the theory of technical stability, Proceedings of the N. Zhukovskiy Military-Air. Academy, Vyp., vol. 135, 1945, pp. 47-60.
26. A.D. Myshkis, and A.M. Samoilenko Systems with impulses in the present instants Mat. Sb. 74 2 1967 202 208
27. S.G. Pandit On the stability of impulsively perturbed differential systems Bull. Austral. Math. Soc. 17 3 1977 423 432
28. S.G. Pandit Differential systems with impulse perturbations Pacific J. Math. 86 2 1980 553 560
29. T. Pavlidis Stability of a class of discontinuous dynamical systems Inform. Control 9 6 1966 298 322
30. T. Pavlidis, and E.I. Jury Analysis of new class of pulse-frequency modulated feed-back systems IEEE Trans. Automat. Control AC10 1 1965 35 43
31. V. Raghavendra, and R.R. Mohana On the stability of differential systems with respect to impulsive perturbations J. Math. Anal. Appl. 48 2 1974 515 526
32. M.R. Mohana Rao, and V. Sree Har Rao Stability of impulse by perturbed systems Bull. Austral. Math. Soc. 16 1 1976 99 110
33. A.M. Samoilenko, and S.D. Borysenko Integro-sum inequalities and stability of processes with discrete disturbances Proceedings of Third International Conference on Differential Equations and Applications Russia, Bulgaria 1987 377 380
34. A.M. Samoilenko, and S.D. Borysenko On functional inequalities of Bihary type for discontinuous functions Uspekhi Mat. Nauk 53 4 1998 147 148
35. A.M. Samoilenko, S.D. Borysenko, C. Cattani, G. Matarazzo, and V. Yasinsky Differential Models: Stability, Inequalities and Estimates 2001 Naukova Dumka Kyiv
36. A.M. Samoilenko, S.D. Borysenko, C. Cattani, and V. Yasinsky Differential Models: Construction, Representations and Applications 2001 Naukova Dumka Kyiv
37. A.M. Samoilenko, S.D. Borysenko, E. Laserra, and G. Matarazzo Wendroff type integro-sum inequalities and applications Math. Notes 3 2 2002 123 132
38. A.M. Samoilenko, and N. Perestyuk Differential Equations with Impulse Effect 1987 Visha Shkola Kyiv
39. V. Sree Har Rao Asymptotically of measure differential equations Nonlinear Anal. Theory Methods Appl. 27 2 1978 483 489