Spectral conditions and an explicit expression for the stabilization of hybrid systems in the presence of feedback delays
Authors:
K. L. Cooke, J. Turi and G. Turner
Journal:
Quart. Appl. Math. 51 (1993), 147-159
MSC:
Primary 93D15
DOI:
https://doi.org/10.1090/qam/1205943
MathSciNet review:
MR1205943
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Abstract: We consider the effect of feedback delays in the stabilization of linear time-invariant plants with sampled outputs. In particular, we obtain an estimate on the “minimum” sampling frequency (in terms of the spectrum of the plant and the delay in the feedback mechanism) needed for stabilization and provide an explicit expression for a stabilizing feedback control.
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- Jiong Min Yong and Aristotle Arapostathis, Stabilization of discrete-time linear systems with a time delay in the feedback loop, Internat. J. Control 48 (1988), no. 4, 1475–1485. MR 964774, DOI https://doi.org/10.1080/00207178808906263
E. J. Barbeau, Polynomials, Springer-Verlag, New York, 1989
K. L. Cooke and J. Wiener, Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl. 99, 265–297 (1984)
B. A. Francis and T. T. Georgiou, Stability theory for linear time-invariant plants with periodic digital controllers, IEEE Trans. Autom. Control AC-33, 820–832 (1988)
I. Gyori and G. Ladas, Oscillation theory of delay differential equations with applications, Oxford University Press, 1991
P. T. Kamamba, Control of linear systems using generalized sampled-data hold functions, IEEE Trans. Autom. Control AC-32, 772–783 (1987)
P. Lancaster and M. Tismenetsky, The Theory of Matrices, Academic Press, Ontario, FL, 1985
M. Marden, Geometry of polynomials, Math. Surveys, No. 3, Amer. Math. Soc., Providence, RI, 1966
Q. G. Mohammed, On the zeros of polynomials, Amer. Math. Monthly 72, 631–633 (1965)
E. D. Sontag, Mathematical Control Theory, Springer-Verlag, New York, 1990
J. Wiener and K. L. Cooke, Oscillations in systems of differential equations with piecewise constant argument, J. Math. Anal. Appl. 137, 221–239 (1989)
Y. Yong, Stabilization of linear systems by time-delay feedback controls, Quart. Appl. Math. 45, 377–388 (1987)
J. Yong, Stabilization of linear systems by time-delay feedback controls. II, Quart. Appl. Math. 56, 593–603 (1988)
J. Yong and A. Araposthathis, Stabilization of discrete-time linear systems with a time delay in the feedback loop, Internat. J. Control 48, 1475–1485 (1988)
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Article copyright:
© Copyright 1993
American Mathematical Society
