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.
Issue Section:
Technical Papers
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
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