This paper gives a broad overview of the stability and control of time-delay systems. Emphasis is on the more recent progress and engineering applications. Examples of practical problems, mathematical descriptions, stability and performance analysis, and feedback control are discussed.

1.
Kolmanovskii, V. B., and Nosov, V. R., 1986, Stability of Functional Differential Equations, Mathematics in Science and Eng., 180, Academic Press, New York.
2.
Bellman, R., and Cooke, K. L., 1963, Differential-Difference Equations, Academic Press, New York.
3.
Malek-Zavarei, M., and Jamshidi, M., 1987, Time Delay Systems: Analysis, Optimization and Applications, North-Holland Systems and Control Series, 9, Amsterdam.
4.
Go´recki, H., Fuksa, S., Grabowski, P., and Korytowski, A., 1989, Analysis and Synthesis of Time-Delay Systems, Polish Scientific Publishers, Warszawa.
5.
Hale, J. K., and Verduyn Lunel, S. M., 1993, Introduction to Functional Differential Equations, Springer-Verlag, New York.
6.
Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., 1994, Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia.
7.
Zhou, K., Doyle, J. C., and Glover, K., 1996, Robust and Optimal Control, Prentice Hall.
8.
Niculescu, S.-I., 2001, Delay Effects on Stability: A Robust Control Approach, Springer-Verlag, Heidelberg, Germany.
9.
Boukas, E.-K., and Liu, Z. K., 2001, Deterministic and Stochastic Time-Delayed Systems, Birkhauser, Boston.
10.
Gu, K., Kharitonov, V., and Chen, J., 2003, Stability of Time-Delay Systems, Birkhauser, Boston.
11.
Kolmanovskii, V., and Myshkis, A., 1999, Introduction to the Theory and Applications of Functional Differential Equations, Kluwer, Dordrecht, The Netherlands.
12.
Ziegler
,
J. G.
, and
Nichols
,
N. B.
,
1942
, “
Optimum Settings for Automatic Controllers
,”
Trans. ASME
,
pp.
759
768
.
13.
Tobias, S. A., 1965, Machine Tool Vibrations, Blackie, London.
14.
Moon, F. C., and Johnson, M. A., 1998, “Nonlinear Dynamics and Chaos in Manufacturing Process,” Dynamics and Chaos in Manufacturing Process, F. C. Moon, ed., Wiley, New York, pp. 3–32.
15.
Ste´pa´n, G., 1998, “Delay-Differential Equation Models for Machine Tool Chatter,” Dynamics and Chaos in Manufacturing Process, F. C. Moon, ed., Wiley, New York, pp. 165–192.
16.
Sbarbaro-Hofer
,
D.
,
1993
, “
Neural Control of a Steel Rolling Mill
,”
IEEE Control Syst. Mag.
,
13
(
3
), pp.
69
75
.
17.
Dorf, R. C., and Kusiak, A., 1994, Handbook of Manufacturing and Automation, Wiley, New York.
18.
Tlusty
,
J.
, and
Ismail
,
F.
,
1983
, “
Special Aspects of Chatter in Milling
,”
ASME J. Vib., Acoust., Stress, Reliab. Des.
,
105
, pp.
24
32
.
19.
Yuan, L., Ja¨rvenpa¨a¨, V.-M., and Keshkinen, E., 2001, “Stability Analysis of Roll Grinding Delay System,” 3rd IFAC Workshop on Time Delay Systems, Santa Fe, NM, pp. 59–63.
20.
Moon, F. C., ed., 1998, Dynamics and Chaos in Manufacturing Process, Wiley, New York.
21.
Kao
,
M.
, and
Moskwa
,
J. J.
,
1995
, “
Turbocharged Diesel Engine Modeling for Nonlinear Engine Control and State Estimation
,”
ASME J. Dyn. Syst., Meas., Control
,
117
, pp.
20
30
.
22.
Cook
,
J. A.
, and
Powell
,
B. K.
, 1988, “Modeling of an Internal Combustion Engine for Control Analysis,” IEEE Control Syst. Mag., pp. 20–25.
23.
Brayton
,
R.
,
1967
, “
Nonlinear Oscillations in a Distributed Network
,”
Q. Appl. Math.
,
24
, pp.
289
301
.
24.
Halanay
,
A.
, and
Raˇsvan
,
V.
,
1997
, “
Stability Radii for Some Propagation Models
,”
IMA J. Math. Contr. Information
,
14
, pp.
95
107
.
25.
Anderson
,
J. A.
, and
Spong
,
M. W.
,
1989
, “
Bilateral Control of Teleoperators With Time Delay
,”
IEEE Trans. Autom. Control
,
34
, pp.
494
501
.
26.
Niemeyer
,
G.
, and
Slotine
,
J.-J. E.
,
1991
, “
Stable Adaptive Teleoperation
,”
IEEE J. Ocean. Eng.
,
16
, pp.
152
162
.
27.
Niemeyer, G., and Slotine, J.-J. E., 1997, “Designing Force Reflecting Teleoperators With Large Time Delays to Appear as Virtual Tools,” Proc. 1997 IEEE ICRA, Albuquerque, NM, pp. 2212–2218.
28.
Izmailov
,
R.
,
1996
, “
Analysis and Optimization of Feedback Control Algorithms for Data Transfers in High-Speed Networks
,”
SIAM J. Control Optim.
,
34
, pp.
1767
1780
.
29.
Bolot, J.-C., and Shankat, A. U., 1992, “Analysis of a Fluid Control Approximation to Flow Control Dynamics,” Proc. IEEE Infocom’92, Florence, Italy, pp. 2398–2407.
30.
Youcef-Toumi, K., and Reddy, S., 1990, “Stability Analysis of Time Delay Control With Application to High Speed Magnetic Bearings,” MIT Laboratory for Manufacturing and Productivity, Report No. LMP-90-004, March, and ASME Winter Annual Meeting.
31.
Olgac
,
N.
, and
Holm-Hansen
,
B. T.
,
1994
, “
A Novel Active Vibration Absorption Technique: Delayed Resonator
,”
J. Sound Vib.
,
176
, pp.
93
104
.
32.
Pyragas
,
K.
,
1992
, “
Continuous Control of Chaos by Self-Controlling Feedback
,”
Phys. Lett. A
,
170
, pp.
421
428
.
33.
Pyragas
,
K.
,
1995
, “
Control of Chaos via Extended Delay Feedback
,”
Phys. Lett. A
,
206
, pp.
323
330
.
34.
Yang
,
B.
, and
Mote
,
C. D.
,
1992
, “
On Time Delay in Noncolocated Control of Flexible Mechanical Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
114
, pp.
409
415
.
35.
Ergen
,
W. K.
,
1954
, “
Kinetics of the Circulating-Fuel Nuclear Reactor
,”
J. Appl. Phys.
,
25
, pp.
702
711
.
36.
Crocco
,
L.
,
1951
, “
Aspects of Combustion Stability in Liquid Propellant Rocket Motors, Part I: Fundamentals—Low Frequency Instability With Monopropellants
,”
J. Am. Rocket Soc.
,
21
, pp.
163
178
.
37.
Abdallah, C., Birdwell, J., Chiasson, J., Chupryna, V., Tang, Z., and Wang, T., 2001, “Load Balancing Instabilities due to Time Delays in Parallel Computations,” 3rd IFAC Workshop on Time Delay Systems, Santa Fe, NM.
38.
Ste´pa´n, G., 1989, Retarded Dynamical Systems: Stability and Characteristic Function, Wiley, New York.
39.
Niculescu, S.-I., Verriest, E. I., Dugard, L., and Dion, J.-M., 1997, “Stability and Robust Stability of Time-Delay Systems: a Guided Tour,” Stability and Control of Time-Delay Systems, L. Dugard and E. I. Verriest, eds., LNCIS 228, pp. 1–71.
40.
Kolmanovskii, V. B., Niculescu, S.-I., and Gu, K., 1999, “Delay Effects on Stability: a Survey,” Proc. 38th IEEE Conf. Decision and Control, Phoenix, AZ, pp. 1993–1998.
41.
Kharitonov, V. L., 1999, “Robust Stability Analysis of Time Delay Systems: A Survey,” Annual Reviews in Control, 23, pp. 185–196.
1.
Pontryagin
,
L. S.
,
1942
, “
On the Zeros of Some Elementary Transcendental Functions,” (Russian)
Izv. Akad. Nauk SSR, Ser. Mat.
,
6
, pp.
115
134
2.
(English translation,
Am. Math. Soc. Trans.
,
1
, pp.
95
110
(
1955
)).
1.
Silva
,
G. J.
,
Datta
,
A.
, and
Bhattacharyya
,
S. P.
,
2002
, “
New Results on the Synthesis of PID Controllers
,”
IEEE Trans. Autom. Control
,
47
(
2
), pp.
241
252
.
2.
Rekasius, Z. V., 1980, “A Stability Test for Systems With Delays,” Proc. of Joint Automatic Control Conf., Paper No. TP9-A.
3.
Olgac
,
N.
, and
Sipahi
,
R.
,
2002
, “
An Exact Method for the Stability Analysis of Time-Delayed LTI Systems
,”
IEEE Trans. Autom. Control
,
47
(
5
), pp.
793
797
.
4.
Walton
,
K.
, and
Marshall
,
J. E.
,
1987
, “
Direct Method for TDS Stability Analysis
,”
IEE Proc. D. Control Theory Appl.
,
134
(
2
), pp.
101
107
.
5.
Cooke
,
K. L.
, and
van den Driessche
,
P.
, 1986, “On Zeros of Some Transcendental Equations,” Funkcialaj Ekvacioj, 29, pp. 77–90.
6.
Chen
,
J.
,
1995
, “
On Computing the Maximal Delay Intervals for Stability of Linear Delay Systems
,”
IEEE Trans. Autom. Control
,
40
, pp.
1087
1093
.
7.
Chen
,
J.
, and
Latchman
,
H. A.
,
1995
, “
Frequency Sweeping Tests for Stability Independent of Delay
,”
IEEE Trans. Autom. Control
,
40
, pp.
1640
1645
.
8.
Huang
,
Y.-P.
, and
Zhou
,
K.
,
2000
, “
On the Robustness of Uncertain Time-Delay Systems With Structured Uncertainties
,”
Syst. Control Lett.
,
41
, pp.
367
376
.
9.
Chen
,
J.
,
Gu
,
G.
, and
Nett
,
C. N.
,
1995
, “
A New Method for Computing Delay Margins for Stability of Linear Delay Systems
,”
Syst. Control Lett.
,
26
, pp.
107
117
.
10.
Chiasson, J., and Abdallah, C. T., 2001, “Robust Stability of Time Delay Systems: Theory,” 3rd IFAC Workshop on Time Delay System, Santa Fe, NM.
11.
Louisell, J., 1997, “Numerics of the Stability Exponent and Eigenvalue Abscissas of a Matrix Delay System,” Stability and Control of Time-Delay Systems, L. Dugard and E. I. Verriest, eds., Lecture Notes in Control and Information Sciences 228, Springer-Verlag, pp. 140–157.
12.
Louisell, J., 1997, “Accurate Determination of the Stability Exponent and Eigenvalue Abscissas in a Linear Delay-Differential System,” Proc. of 4th European Control Conf., Brussels.
13.
Louisell
,
J.
,
1995
, “
Absolute Stability in Linear Delay-Differential Systems: Illposedness and Robustness
,”
IEEE Trans. Autom. Control
,
40
, pp.
1288
1291
.
14.
Scorletti, G., 1997, “Robustness Analysis With Time-Delay,” 36th IEEE Conf. Dec. Cont., San Diego, pp. 3824–2829.
15.
Jun, M., and Safanov, M., 2001, “Rational Multiplier IQC’s for Uncertain Time-Delays and LMI Stability Conditions,” 40th IEEE Conf. Dec. Contr., Orlando, FL, pp. 3196–3201.
16.
Gu
,
K.
, and
Niculescu
,
S.-I.
,
2000
, “
Additional Dynamics in Transformed Time-Delay Systems
,”
IEEE Trans. Autom. Control
,
45
, pp.
572
575
.
17.
Kharitonov
,
V. L.
,
1978
, “
Asymptotic Stability of an Equilibrium Position of a Family of System of Linear Differential Equations
,”
Diff. Eq.
,
14
, pp.
2086
2088
.
18.
Fu
,
M.
,
Olbrot
,
A. W.
, and
Polis
,
M. P.
,
1989
, “
Robust Stability for Time-Delay Systems: The Edge Theorem and Graphical Test
,”
IEEE Trans. Autom. Control
,
AC-34
, pp.
813
820
.
19.
Fu
,
M.
,
Olbrot
,
A. W.
, and
Polis
,
M. P.
,
1991
, “
Edge Theorem and Graphical Test for Robust Stability of Neutral Time-Delay Systems
,”
Automatica
,
27
, pp.
739
742
.
20.
Kharitonov
,
V. L.
, and
Zhabko
,
A. P.
,
1994
, “
Robust Stability of Time-Delay Systems
,”
IEEE Trans. Autom. Control
,
AC-39
, pp.
2388
2397
.
21.
Youcef-Toumi
,
K.
, and
Bobbett
,
J.
,
1991
, “
Stability of Uncertain Linear Systems With Time Delay
,”
ASME J. Dyn. Syst., Meas., Control
,
113
, pp.
558
567
.
22.
Santos, J., Mondie´, S., and Kharitonov, V., 2001, “Matrix Convex Directions for Time Delay Systems,” 3rd IFAC Workshop on Time Delay Systems, Santa Fe, NM.
23.
Cohen
,
N.
, and
Kogan
,
J.
,
1996
, “
Convexity of a Frequency Response Arc Associated With a Stable Entire Function
,”
IEEE Trans. Autom. Control
,
41
, pp.
295
299
.
24.
Krasovskii, N. N., 1959, Stability of Motion, [Russian] Moscow (English Translation, Stanford University Press, 1963).
25.
Kokame
,
H.
,
Kobayashi
,
H.
, and
Mori
,
T.
,
1998
, “
Robust H Performance for Linear Delay-Differential Systems With Time-Varying Uncertainty
,”
IEEE Trans. Autom. Control
,
43
, pp.
223
226
.
26.
Niculescu, S.-I., Neto, A. T., Dion, J.-M., and Dugard, L., 1995, “Delay-Dependent Stability of Linear Systems With Delayed State: an LMI Approach,” Proc. 34th IEEE Conf. on Decision and Control, pp. 1495–1497.
27.
Li
,
X.
, and
de Souza
,
C. E.
,
1997
, “
Delay-Dependent Robust Stability and Stabilization of Uncertain Time-Delay Systems: a Linear Matrix Inequality Approach
,”
IEEE Trans. Autom. Control
,
42
, pp.
1144
1148
.
28.
Kolmanovskii
,
V. B.
,
Niculescu
,
S.-I.
, and
Richard
,
J.-P.
,
1999
, “
On the Liapunov-Krasovskii Functionals for Stability Analysis of Linear Delay Systems
,”
Int. J. Control
,
72
, pp.
374
384
.
29.
Kolmanovskii
,
V. B.
, and
Richard
,
J. P.
, 1997, “Stability of Some Systems With Distributed Delays,” JESA, 31, pp. 971–982.
30.
Verriest, E. I., 1999, “Linear Systems With Rational Distributed Delay: Reduction and Stability,” 1999 European Control Conf., Karlsruhe, Germany.
31.
Kharitonov
,
V. L.
, and
Melchor-Aguilar
,
D.
,
2000
, “
On Delay-Dependent Stability Conditions
,”
Syst. Control Lett.
,
40
, pp.
71
76
.
32.
Kharitonov, V. L., and Melchor-Aguilar, D., 2001, “Additional Dynamics for Time Varying Delay Systems,” 40th IEEE Conf. on Decision and Control, Orlando, FL.
33.
Gu
,
K.
, and
Niculescu
,
S.-I.
,
2001
, “
Further Remarks on Additional Dynamics in Various Model Transformations of Linear Delay Systems
,”
IEEE Trans. Autom. Control
,
46
, pp.
497
500
.
34.
Park
,
P.
,
1999
, “
A Delay-Dependent Stability for Systems With Uncertain Time-Invariant Delays
,”
IEEE Trans. Autom. Control
,
44
, pp.
876
877
.
35.
Repin
,
Y. M.
,
1965
, “
Quadratic Lyapunov Functionals for Systems With Delay,” (Russian)
Prikl. Mat. Mekh.
,
29
, pp.
564
566
.
36.
Datko, R., 1972, “An Algorithm for Computing Liapunov Functionals for Some Differential Difference Equations,” Ordinary Differential Equations, L. Weiss, ed., Academic Press, pp. 387–398.
37.
Infante
,
E. F.
, and
Castelan
,
W. V.
,
1978
, “
A Lyapunov Functional for a Matrix Difference-Differential Equation
,”
J. Diff. Eqns.
,
29
, pp.
439
451
.
38.
Huang
,
W.
,
1989
, “
Generalization of Liapunov’s Theorem in a Linear Delay System
,”
J. Math. Anal. Appl.
,
142
, pp.
83
94
.
39.
Fridman
,
E.
, and
Shaked
,
U.
,
1999
, “
H-Norm and Invariant Manifolds of Systems With State Delays
,”
Syst. Control Lett.
,
36
, pp.
157
165
.
40.
Fridman
,
E.
, and
Shaked
,
U.
, “Finite Horizon H∞ State-Feedback Control of Continuous-Time Systems With State Delays,” IEEE Trans. Autom. Control, 45, pp. 2406–2411.
41.
Gu
,
K.
,
2001
, “
A Further Refinement of Discretized Lyapunov Functional Method for the Stability of Time-Delay Systems
,”
Int. J. Control
,
74
, pp.
967
976
.
42.
Gu, K., 2001, “Refined Discretized Lyapunov Functional Method for Systems With Multiple Delays,” 40th Conf. on Decision and Control, Orlando, FL.
43.
Gu, K., 2001, “An Improved Stability Criterion for Systems With Distributed Delays,” 3rd IFAC Workshop on Time Delay Systems, Santa Fe, NM.
44.
Han
,
Q.-L.
, and
Gu
,
K.
,
2001
, “
On Robust Stability of Time-Delay Systems With Norm-Bounded Uncertainty
,”
IEEE Trans. Autom. Control
,
46
, pp.
1426
1431
.
45.
Phoojaruenchanachai
,
S.
, and
Furuta
,
K.
,
1992
, “
Memoryless Stabilization of Uncertain Linear Systems Including Time-Varying State Delays
,”
IEEE Trans. Autom. Control
,
37
, pp.
1022
1026
.
46.
Cao
,
Y.-Y.
, and
Sun
,
Y.-X.
,
1998
, “
Robust Stabilization of Uncertain Systems With Time-Varying Multistate Delays
,”
IEEE Trans. Autom. Control
,
43
, pp.
1484
1488
.
47.
Kim
,
J.-H.
,
2001
, “
Delay and its Time-Derivative Dependent Robust Stability of Time-Delayed Linear Systems With Uncertainty
,”
IEEE Trans. Autom. Control
,
46
, pp.
789
792
.
48.
Gu, K., and Han, Q.-L., 2000, “Discretized Lyapunov Functional for Linear Uncertain Systems With Time-Varying Delay,” 2000 American Control Conf., Chicago.
49.
Razumikhin
,
B. S.
,
1956
, “
On the Stability of Systems With a Delay,” (Russian
),
Prikl. Mat. Mekh.
,
20
, pp.
500
512
.
50.
Razumikhin
,
B. S.
, 1960, “Application of Liapunov’s Method to Problems in the Stability of Systems With a Delay,” (Russian), Automat i Telemeh, 21, pp. 740–749.
51.
Thowsen
,
A.
,
1983
, “
Uniform Ultimate Boundedness of the Solutions of Uncertain Dynamic Delay Systems With State-Dependent and Memoryless Feedback Control
,”
Int. J. Control
,
37
, pp.
1135
1143
.
52.
Li
,
X.
, and
de Souza
,
C. E.
,
1997
, “
Criteria for Robust Stability and Stabilization of Uncertain Linear Systems With State Delay
,”
Automatica
,
33
, pp.
1657
1662
.
53.
Cao
,
Y.-Y.
,
Sun
,
Y.-X.
, and
Cheng
,
C.
,
1998
, “
Delay-Dependent Robust Stabilization of Uncertain Systems With Multiple State Delays
,”
IEEE Trans. Autom. Control
,
43
, pp.
1608
1612
.
54.
Gu, K., and Han, Q.-L., 2001, “A Revisit of Some Delay-Dependent Stability Criteria for Uncertain Time-Delay Systems,” 3rd IFAC Workshop on Time Delay Systems, Santa Fe, NM.
55.
Shaked
,
U.
,
Yaesh
,
I.
, and
de Souza
,
C. E.
,
1998
, “
Bounded Real Criteria for Linear Time-Delay Systems
,”
IEEE Trans. Autom. Control
,
43
(
7
), pp.
1016
1022
.
56.
De Souza
,
C. E.
, and
Li
,
X.
,
1999
, “
Delay-Dependent Robust H Control of Uncertain Linear State-Delayed Systems
,”
Automatica
,
35
, pp.
1313
1321
.
57.
Zhang
,
J.
,
Knopse
,
C. R.
, and
Tsiotras
,
P.
,
2001
, “
Stability of Time-Delay Systems: Equivalence Between Lyapunov and Scaled Small-Gain Conditions
,”
IEEE Trans. Autom. Control
,
46
, pp.
482
486
.
58.
Halanay, A., 1966, Differential Equations: Stability, Oscillations, Time-Lags, Academic Press, New York.
59.
Lakshmikantham, V., and Leela, S., 1969, Differential and Integral Inequalities, Academic Press, New York.
60.
Louisell
,
J.
,
1992
, “
Growth Estimates and Asymptotic Stability for a Class of Differential-Delay Equation Having Time-Varying Delay
,”
J. Math. Anal. Appl.
,
164
, pp.
453
479
.
61.
Lehman, B. and Weibel, S. P., 1999, “Partial Averaging of Functional Differential Equations,” Proc. of 38th Conf. on Decision and Control, Phoenix, AZ, pp. 4684–4689.
62.
Olgac
,
N.
,
Elmali
,
H.
, and
Vijayan
,
S.
,
1996
, “
Introduction to the Dual Frequency Fixed Delayed Resonator
,”
J. Sound Vib.
,
189
, pp.
355
367
.
63.
Olgac
,
N.
,
Elmali
,
H.
,
Hosek
,
M.
, and
Renzulli
,
M.
,
1997
, “
Active Vibration Control of Distributed Systems Using Delayed Resonator With Acceleration Feedback
,”
ASME J. Dyn. Syst., Meas., Control
,
119
, pp.
380
389
.
64.
Filipovic´, D., and Olgac, N., 1997, “Delayed Resonator With Speed Feedback Including Dual Frequency-Theory and Experiment,” Proc. 36th Conf. Dec. and Control, San Diego, pp. 2535–2540.
65.
Jalili, N., and Olgac, N., 1998, “Stability Analysis of Multiple Delayed Resonator Vibration Absorbers,” Dynamics, Acoustics and Simulations, ASME Winter Annual Meeting, DE-Vol. 98, pp. 211–217.
66.
Youcef-Toumi
,
K.
, and
Reddy
,
S.
,
1992
, “
Analysis of Linear Time Invariant Systems With Time Delay
,”
ASME J. Dyn. Syst., Meas., Control
,
114
, pp.
544
555
.
67.
Youcef-Toumi
,
K.
, and
Wu
,
S.-T.
,
1992
, “
Input/Output Linearization Using Time Delay Control
,”
ASME J. Dyn. Syst., Meas., Control
,
114
, pp.
10
19
.
68.
Yang
,
B.
,
1992
, “
Noncolocated Control of a Damped String Using Time Delay
,”
ASME J. Dyn. Syst., Meas., Control
,
114
, pp.
736
740
.
69.
Nakajima
,
H.
,
1997
, “
On Analytical Properties of Delayed Feedback Control of Chaos
,”
Phys. Lett. A
,
232
, pp.
207
210
.
70.
Nakajima
,
H.
, and
Ueda
,
Y.
,
1998
, “
Limitation of Generalized Delayed Feedback Control
,”
Physica D
,
111
, pp.
143
150
.
71.
Kokame
,
H.
,
Hirata
,
K.
,
Konishi
,
K.
, and
Mori
,
T.
,
2001
, “
State Difference Feedback for Stabilizing Uncertain Steady States of Non-Linear Systems
,”
Int. J. Control
,
74
, pp.
537
546
.
72.
Mazenc
,
F.
,
Mondie´
,
S.
, and
Niculescu
,
S.-I.
,
2001
, “
Global Asymptotic Stabilization for Chains of Integrators With a Delay in the Input
,”
IEEE Trans. Autom. Control
,
48
, pp.
57
63
.
73.
Abdallah, C. T., Dorato, P., Benı´tez-Read, J., and Byrne R., 1993, “Delayed Positive Feedback can Stabilize Oscillatory Systems,” Proc. of the American Control Conf., San Francisco, pp. 3106–3107.
74.
Smith
,
O. J. M.
,
1959
, “
A Controller to Overcome Dead Time
,”
Instrument Society of America Journal
,
6
, pp.
28
33
.
75.
Matausˇek
,
M. R.
, and
Micicˇ
,
A. D.
,
1999
, “
On the Modified Smith Predictor for Controlling a Process With an Integrator and Long Dead-Time
,”
IEEE Trans. Autom. Control
,
44
(
8
), pp.
1603
1606
.
76.
Zhang
,
W.
,
Sun
,
Y.
, and
Xu
,
X.
,
1998
, “
Two Degree-of-Freedom Smith Predictor for Processes With Time Delay
,”
Automatica
,
34
(
10
), pp.
1279
1282
.
77.
Artstein
,
Z.
,
1982
, “
Linear Systems With Delayed Control: a Reduction
,”
IEEE Trans. Autom. Control
,
AC-27
, pp.
869
879
.
78.
Olbrot
,
A. W.
,
1978
, “
Stabilizability, Detectability, and Spectrum Assignment for Linear Autonomous Systems With General Time Delays
,”
IEEE Trans. Autom. Control
,
AC-23
(
5
), pp.
887
890
.
79.
Manitius
,
A. Z.
, and
Olbrot
,
A. W.
,
1979
, “
Finite Spectrum Assignment Problem for Systems With Delay
,”
IEEE Trans. Autom. Control
,
AC-24
(
4
), pp.
541
553
.
80.
Wang, Q.-G., Lee, T. H., and Tan, K. K., 1998, Finite Spectrum Assignment for Time-Delay Systems, LNCIS, 239, Springer-Verlag, London.
81.
Michiels, W., Engelborghs, K., Vansevenant, P., and Roose, D., 2000, “Continuous Pole Placement Method for Delay Equations,” Proc. of 2nd IFAC Workshop on Linear Time Delay Systems, Ancona, Italy, pp. 129–134.
82.
Mirkin, L., 2000, “On the Extraction of Dead-Time Controllers From Delay-Free Parametrizations,” 2nd IFAC Workshop on Linear Time Delay Systems, Ancona, Italy.
83.
Meinsma
,
G.
, and
Zwart
,
H.
,
2000
, “
On H Control for Dead Time Systems
,”
IEEE Trans. Autom. Control
,
45
, pp.
272
285
.
84.
Zhong
,
Q.-C.
,
2003
, “
H Control of Dead-Time Systems Based on a Transformation
,”
Automatica
,
39
(
2
), pp.
361
366
.
85.
Shujaee
,
K.
, and
Lehman
,
B.
,
1997
, “
Vibrational Feedback Control of Time Delay Systems
,”
IEEE Trans. Autom. Control
,
42
(
11
), pp.
1529
1545
.
86.
Tadmor
,
G.
,
1997
, “
Robust Control in the Gap: a State-Space Solution in the Presence of a Single Input Delay
,”
IEEE Trans. Autom. Control
,
42
(
9
), pp.
1330
1335
.
87.
Ohta
,
Y.
, and
Kojima
,
A.
,
1999
, “
Formulas for Hankel Singular Values and Vectors for a Class of Input Delay Systems
,”
Automatica
,
35
, pp.
201
215
.
88.
Niculescu, S.-I., Fu, M., and Li, H., 1997, “Delay-Dependent Closed-Loop Stability of Linear Systems With Input Delays: An LMI Approach,” Proc. of 36th IEEE Conf. Dec. Contr., San Diego, pp. 1623–1628.
89.
Jankovic
,
M.
,
2001
, “
Control Lyapunov-Razumikhin Functions and Robust Stabilization of Time-Delay Systems
,”
IEEE Trans. Autom. Control
,
46
, pp.
1048
1060
.
90.
El-Khazali
,
R.
,
1998
, “
Variable Structure Robust Control of Uncertain Time-Delay Systems
,”
Automatica
,
34
(
3
), pp.
327
332
.
91.
Fridman
,
E.
,
Fridman
,
L.
, and
Shustin
,
E.
,
2000
, “
Steady Modes in Relay Control Systems With Time Delay and Periodic Disturbances
,”
ASME J. Dyn. Syst., Meas., Control
,
122
, pp.
732
737
.
92.
Gouaisbaut, F., Dambrine, M., and Richard, J.-P., 2001, “Sliding Mode Control of Systems With Distributed Delay,” 3rd IFAC Workshop on Time Delay Systems, Santa Fe, NM.
93.
Song, Y., Yu, X., Chen, G., and Xu, J.-X., 2001, “Repetitive Learning Time-Delayed Control for Chaotic Systems,” 3rd IFAC Workshop on Time Delay Systems, Santa Fe, NM.
94.
Chen
,
Y.
,
Gong
,
Z.
, and
Wen
,
C.
,
1998
, “
Analysis of a High-Order Iterative Learning Control Algorithm for Uncertain Nonlinear Systems With State Delays
,”
Automatica
,
34
, pp.
345
353
.
95.
Kubo
,
T.
, and
Shimemura
,
E.
,
1999
, “
Gain and Phase Margin of Optimal Memoryless Regulator of Systems With Time-Delay
,”
Int. J. Control
,
72
, pp.
404
410
.
96.
Park
,
P.
,
Moon
,
Y. S.
, and
Kwon
,
W. H.
,
1999
, “
A Stabilizing Output-Feedback Linear Quadratic Control for Pure Input-Delayed Systems
,”
Int. J. Control
,
72
, pp.
385
391
.
97.
Olbrot
,
A. W.
,
1973
, “
Algebraic Criteria of Controllability to Zero Function for Linear Constant Time-Lag Systems
,”
Control and Cybernetics
,
2
, pp.
59
77
.
98.
Huang
,
Y.-P.
, and
Zhou
,
K.
,
2000
, “
Robust Stability of Uncertain Time-Delay Systems
,”
IEEE Trans. Autom. Control
,
45
, pp.
2169
2173
.
99.
Engelborghs
,
K.
,
Dambrine
,
M.
, and
Roose
,
D.
,
2001
, “
Limitation of a Class of Stabilization Methods for Delay Systems
,”
IEEE Trans. Autom. Control
,
46
(
2
), pp.
336
339
.
You do not currently have access to this content.