Stabilization of linear systems by time-delay feedback controls. II
Author:
Jiong Min Yong
Journal:
Quart. Appl. Math. 46 (1988), 593-603
MSC:
Primary 93D15; Secondary 34K20, 93C05
DOI:
https://doi.org/10.1090/qam/973377
MathSciNet review:
973377
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Abstract: The notion of uniform $r$-stabilizability for linear autonomous systems is introduced. Some abstract characterizations and easy-to-check necessary conditions and sufficient conditions are given.
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- Jiong Min Yong, Stabilization of linear systems by time-delay feedback controls, Quart. Appl. Math. 45 (1987), no. 2, 377–388. MR 895105, DOI https://doi.org/10.1090/S0033-569X-1987-0895105-3
R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York, London, 1963
R. Datko, A procedure for determination of the exponential stability of certain differential-difference equations, Quart. Appl. Math. 36, 279–292 (1978)
L. E. El’sgol’ts and S. B. Norkin, Introduction to the Theory and Application of Differential Equations with Deviating Arguments, Academic Press, New York, London, 1973
J. K. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, Berlin, 1977
J. K. Hale, E. F. Infante and E. P. Tsen, Stability in linear delay equations, J. Math. Anal. Appl. 105, 533–555 (1985)
V. B. Kolmanovskii and V. R. Nosov, Stability of Functional Differential Equations, Academic Press, London, 1986
X.-J. Li, On the absolute stability of systems with time lags, Acta Math. Sinica 13, 558–573 (1963); English transl. in Chinese Math. 4, 609–626 (1963)
J. M. Mahaffy, A test for stability of linear differential delay equations, Quart. Appl. Math. 40, 193–202 (1982)
L. S. Pontryagin, On the zeros of some elementary transcendental functions, Amer. Math. Soc. Transl., Ser. 2, 1, 95–110 (1955)
W. M. Wonham, Linear Multivariate Control: A Geometric Approach, 2nd Edition, Springer-Verlag, New York, 1979
J. Yong, Stabilization of linear systems by time-delay feedback controls, Quart. Appl. Math. 45, 377–388 (1987)
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Article copyright:
© Copyright 1988
American Mathematical Society