Stabilization of linear systems by time-delay feedback controls
Author:
Jiong Min Yong
Journal:
Quart. Appl. Math. 45 (1987), 377-388
MSC:
Primary 93D15; Secondary 34K35
DOI:
https://doi.org/10.1090/qam/895105
MathSciNet review:
895105
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Abstract: The notion of $r$-stabilizability of linear autonomous systems is introduced. If the system $\left [ {A,B} \right ]$ is completely controllable and the spectrum of $A$ is contained in the left half of the complex plane then the system is $r$-stabilizable for any $r > 0$. Finally, a one-dimensional case is discussed.
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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, Functional Differential Equations, Springer-Verlag, New York, Berlin, 1977
J. K. Hale, E. F. Infante, and F. P. Tsen, Stability in linear delay equations, J. Math. Anal. Appl. 105, 535–555 (1985)
N. D. Hayes, Roots of the transcendental equation associated with a certain difference-differential equation, J. London Math. Soc. 25, 226–232 (1950)
Li, Xun-jing, 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)
Yuan-Xun Qin, Iong-qing Liou, and Lian Wang, Effect of time-lags on stability of dynamical systems, Sci. Sinica 9, 719–747 (1960); English transl. in Chinese Math. 9, 169–198 (1967)
W. M. Wonham, Linear multivariable control: A geometric approach, 2nd ed., Springer-Verlag, New York, Heidelberg, Berlin, 1979
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Article copyright:
© Copyright 1987
American Mathematical Society
