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Bernfeld, Stephen R.; Lakshmikantham, V.

Practical stability and Lyapunov functions. (English) Zbl 0438.34040

Tohoku Math. J., II. Ser. 32, 607-613 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0438.34040

Cited in 11 Documents

MSC:

34D20 Stability of solutions to ordinary differential equations

Keywords:

Lyapunov functions; practical stability
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Full Text: DOI

References:

[1] R. W. GUNDERSON, On stability over a finite interval, IEEE Trans. Auto-Control AC-12 (1967), 634-635.
[2] T. HALLAM AND V. KOMKOV, Application of Liapunov’s functions to finite time stability, Rev. Roum. Math. Pures et Appl. 14 (1969), 495-501. · Zbl 0186.15302
[3] A. A. KAYANDE, A Theorem on contractive stability, SIAM J. Appl. Math. 21 (1971), 601-604. JSTOR: · Zbl 0251.34035 · doi:10.1137/0121065
[4] A. A. KAYANDE AND J. S. W. WONG, Finite time stability and comparison principles, Proc. Camb. Phil. Soc. 64 (1968), 749-756. · Zbl 0193.05701 · doi:10.1017/S0305004100043450
[5] V. LAKSHMIKANTHAM AND S. LEELA, Differential and Integral Inequalities, Academi Press, New York, 1966. · Zbl 0189.39902
[6] J. P. LASALLE AND S. LEFSCHETZ, Stability by Lyapunov’s Direct Method with Applica tions, Academic Press, New York, 1961.
[7] L. WEISS AND E. F. INFANTE, On the stability of systems defined over a finite tim interval, Proc. Nat. Acad. Sci. U. S. A. 54 (1965), 44-48. JSTOR: · Zbl 0134.30702 · doi:10.1073/pnas.54.1.44
[8] L. WEISS AND E. F. INFANTE, Finite time stability under perturbing forces and o product spaces, IEEE Trans. Auto. Cont. AC-12 (1967), 54-59. · Zbl 0168.33903 · doi:10.1109/TAC.1967.1098483
[9] L. WEISS, Converse theorems for finite time stability, SIAM J. Appl. Math. 16 (1968), 1319-1324. JSTOR: · Zbl 0175.38103 · doi:10.1137/0116110
[10] T. YOSHIZAWA, Stability Theory by Liapunov’s Second Method, Math. Soc. of Japan, Tokyo, 1966. · Zbl 0144.10802
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