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Hybrid systems on time scales. (English) Zbl 1032.34050
The authors consider hybrid dynamic systems on time scales and give sufficient conditions for the practical stability of the systems in terms of Lyapunov-like functions and the comparison principle.

MSC:
34D20Stability of ODE
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References:
[1] Clark, F. H.; Ledyaev, Yu.S.; Stern, R. I.; Woleski, P. R.: Nonsmooth analysis and control theory. (1998)
[2] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations. (1989) · Zbl 0719.34002
[3] Lakshmikantham, V.; Leela, S.; Martynyuk, A. A.: Practical stability of nonlinear systems. (1990) · Zbl 0753.34037
[4] Lakshmikantham, V.; Liu, X. Z.: Impulsive hybrid systems and stability theory. Internat. J. Nonlinear differential equations 5, 9-17 (1999) · Zbl 0901.34018
[5] Lakshmikantham, V.; Sivasundaram, S.; Kaymakcalan, B.: Dynamic systems on measure chains. (1996) · Zbl 0869.34039
[6] Nerode, A. M.; Kohn, W.: Models in hybrid systems. Lecture notes in computer science 36 (1993)
[7] Otero, D.; Giuliani, D.; Sassano, M.: Temporal dimension and transition out of chaos. Physica A 178, 280-288 (1991)