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Control systems and differential inequalities

Published online by Cambridge University Press:  24 October 2008

V. Lakshmikantham
Affiliation:
University of Rhode Island, Kingston
C. P. Tsokos
Affiliation:
University of Rhode Island, Kingston

Extract

Let J denote the half line 0 ≤ t < ∞, Rn the Euclidian n-space and R+ = [0, ∞). Let ║x║ denote the Euclidian norm of xRn, and S denote the set [x: ║x║ < ρ].

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Bellman, R.Notes on Control Processes. 1. On minimum and maximum deviations. Quart. Appl. Math. 14 (1957), 419423.Google Scholar
(2)Bellman, R.Some aspects of the mathematical theory of control processes. Rand-Corporation, Ch. 4 (1958).Google Scholar
(3)Barbasin, E. A.On the realization of motion along a given trajectory. Automat. i Telmeh 22 (1961), 681687. (Russian.) Translated as Automat. Remote Control 22 (1961), 587–593.Google Scholar
(4)Liberman, L. H.On certain problems of the stability of solutions of nonlinear differential equations in Banach Spaces. (Russian.)Sibirsk. Mat. ž 1 (1960), 611616.Google Scholar
(5)Liberman, L. H.On approximation of solutions of differential operator systems in Hilbert spaces. (Russian.)Mathematica (1964), pp. 8892.Google Scholar
(6)Kayande, A. A. and Miley, D. B.Lyapunov functions and a control problem. Cambridge Proc. Philos. Soc. 63 (1967), 435438.CrossRefGoogle Scholar
(7)LaSalle, J. P. and Rath, T. J.A new concept of stability. Proc. 2nd Congress of IFAC, Basle, 1963 (Butterworth, London).Google Scholar
(8)Lakshmikantham, V.On the boundedness of solutions of non-linear differential equations. Proc. Am. Math. Soc. 8 (1957), 10441048.Google Scholar
(9)Vrkoč, I.Integral stability. (Russian.)Czechoslovak Math. J. 9 (1959), 71128.Google Scholar
(10)Halanay, A.Differential equations, stability, oscillations, time lags, Academic Press (1966).Google Scholar
(11)Coppel, W. A.Stability and Asymptotic behaviour of differential equations. Heath Mathematical Monograph.Google Scholar