×

A feedback control law for nonlinear time lag systems. (English) Zbl 0722.93023

Summary: A simple memoryless state feedback control law is derived for a class of nonlinear time lag systems. Some well known techniques are used to transform a nonlinear time lag system in suitable coordinates in which the design of the control law is straightforward. In certain cases, the asymptotic stability of the closed loop system is ensured independently of delay values.

MSC:

93B52 Feedback control
93C10 Nonlinear systems in control theory
93D20 Asymptotic stability in control theory
Full Text: DOI

References:

[1] Bhat, K. P.M.; Koivo, H. N., An observer theory for time-delay systems, IEEE Trans. Aut. Control AC-21, 266-269 (1976) · Zbl 0328.93023
[2] Brierley, S. D.; Chiasson, J. N.; Lee, E. B.; Zak, S. H., On the stability independent of delay for linear systems, IEEE Trans. Aut. Control AC-27, 252-254 (1982) · Zbl 0469.93065
[3] Brockett, R. W., Feedback invariants for nonlinear systems, Proc. of the 7th IFAC Congress, Helsinki, 1115-1120 (1978) · Zbl 0457.93028
[4] Boothby, W. M., Some comments on global linearization of nonlinear systems, Systems Control Lett., 4, 143-147 (1984) · Zbl 0538.93027
[5] Chiasson, J., A method for computing the interval of delay values for which a differential-delay system is stable, IEEE Trans. Aut. Control AC-33, 1176-1178 (1988) · Zbl 0668.34074
[6] Hahn, W., Stability of Motion (1967), Springer-Verlag: Springer-Verlag Berlin · Zbl 0189.38503
[7] Hewer, G. A.; Nazaroff, G. J., Observer theory for delayed differential equations, Int. J. Control, 18, 1, 1-7 (1973) · Zbl 0266.93006
[8] Hunt, L. R.; Su, R.; Meyer, G., Global transformations of nonlinear systems, IEEE Trans. Aut. Control AC-28, 24-31 (1982) · Zbl 0502.93036
[9] Jacubczyk, B.; Respondek, W., On linearization of control systems, Bull. Acad. Pol. Sci. Ser. Sci. Math., 28, 517-522 (1980) · Zbl 0489.93023
[10] Krener, A. J., On the equivalence of control systems and the linearization of nonlinear systems, SIAM J. Control, 11, 4, 670-676 (1973) · Zbl 0243.93009
[11] Manitius, A.; Olbrot, A. W., Finite spectrum assignment problem for systems with delays, IEEE Trans. Aut. Control AC-24, 541-543 (1979) · Zbl 0425.93029
[12] Mori, T., Criteria for asymptotic stability of linear time-delay systems, IEEE Trans. Aut. Control AC-30, 158-161 (1985) · Zbl 0557.93058
[13] Mori, T.; Kokame, H., Stability of \(ẋ(t)=Ax(t)+Bx(t−t)\), IEEE Trans. Aut. Control AC-34, 460-462 (1989) · Zbl 0674.34076
[14] Olbrot, A. W., Stabilizability, detectability, and spectrum assignment for linear systems with general time delays, IEEE Trans. Aut. Control AC-23, 887-890 (1978) · Zbl 0399.93008
[15] Olbrot, A. W., Observability and observers for a class of linear systems with delays, IEEE Trans. Aut. Control AC-26, 513-517 (1981) · Zbl 0474.93019
[16] Pearson, A. E.; Fiagbedzi, Y. A., Feedback linearization of linear autonomous time lag systems, IEEE Trans. Aut. Control AC-31, 847-855 (1986) · Zbl 0601.93045
[17] Pearson, A. E.; Fiagbedzi, Y. A., An observer for time lag systems, IEEE Trans. Aut. Control AC-34, 775-777 (1989) · Zbl 0687.93011
[18] Su, R., On the linear equivalents of nonlinear systems, Sysem Control Lett., 2, 48-52 (1982) · Zbl 0482.93041
[19] Watanabe, K., Finite spectrum assignment and observer for multivariable systems with commensurate delays, IEEE Trans. Aut. Control AC-31, 543-550 (1986) · Zbl 0596.93009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.