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
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
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.
- Richard Bellman and Kenneth L. Cooke, Differential-difference equations, Academic Press, New York-London, 1963. MR 0147745
- R. Datko, A procedure for determination of the exponential stability of certain differential-difference equations, Quart. Appl. Math. 36 (1978/79), no. 3, 279–292. MR 508772, DOI https://doi.org/10.1090/S0033-569X-1978-0508772-8
- L. E. Èl′sgol′ts and S. B. Norkin, Introduction to the theory and application of differential equations with deviating arguments, Academic Press [A Subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1973. Translated from the Russian by John L. Casti; Mathematics in Science and Engineering, Vol. 105. MR 0352647
- Jack Hale, Theory of functional differential equations, 2nd ed., Springer-Verlag, New York-Heidelberg, 1977. Applied Mathematical Sciences, Vol. 3. MR 0508721
- Jack K. Hale, Ettore F. Infante, and Fu Shiang Peter Tsen, Stability in linear delay equations, J. Math. Anal. Appl. 105 (1985), no. 2, 533–555. MR 778486, DOI https://doi.org/10.1016/0022-247X%2885%2990068-X
- V. B. Kolmanovskiĭ and V. R. Nosov, Stability of functional-differential equations, Mathematics in Science and Engineering, vol. 180, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1986. MR 860947
- Xun-jing Li, On the absolute stability of systems with time lags, Chinese Math. 4 (1963), 609–626. MR 164109
- J. M. Mahaffy, A test for stability of linear differential delay equations, Quart. Appl. Math. 40 (1982/83), no. 2, 193–202. MR 666674, DOI https://doi.org/10.1090/S0033-569X-1982-0666674-3
- L. S. Pontryagin, On the zeros of some elementary transcendental functions, Amer. Math. Soc. Transl. (2) 1 (1955), 95–110. MR 0073686
- W. Murray Wonham, Linear multivariable control: a geometric approach, 2nd ed., Applications of Mathematics, vol. 10, Springer-Verlag, New York-Berlin, 1979. MR 569358
- 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)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
93D15,
34K20,
93C05
Retrieve articles in all journals
with MSC:
93D15,
34K20,
93C05
Additional Information
Article copyright:
© Copyright 1988
American Mathematical Society
