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Generalized Popov theory applied to state-delayed systems. (English) Zbl 0965.93083
The article contains dubious statements, like the one following Theorem 3.1 “\(\dots\) the state \(x(t-\tau)\) may be interpreted as a fictitious input \(f(t)\) \(\dots\)”. In the sentence following equation (17) the claim “\(\dots\) the proposed technique may also be applied to systems with time-varying delays\(\dots\)” needs to be substantiated by restrictive conditions. Nonautonomous ordinal differential equations are rarely equivalent to autonomous ones (of the same order).

93D10 Popov-type stability of feedback systems
93C23 Control/observation systems governed by functional-differential equations
Full Text: DOI
[1] Halanay, A., Differential equations: stability, oscillations, time lags, (1966), Academic Press New York · Zbl 0144.08701
[2] Hale, J.K.; Verduyn Lunel, S.M., Introduction to functional differential equation, (1993), Springer New York · Zbl 0787.34002
[3] Ikeda, M.; Ashida, T., Stabilization of linear systems with time-varying delay, IEEE transactions on automatic control, AC-24, 369-370, (1979) · Zbl 0399.93037
[4] Ionescu, V., Niculescu, S.-I., Dion, J.-M., Dugard, L., & Li, H. (1999). Generalized Popov theory applied to state-delayed systems. Internal Note LAG-1999 (full version of the paper). · Zbl 0965.93083
[5] Ionescu, V.; Oară, C.; Weiss, M., Generalized Riccati theory, (1998), Wiley New York
[6] Lee, J.H.; Kim, S.W.; Kwon, W.H., Memoryless H∞ controllers for state delayed systems, IEEE transactions on automatic control, 39, 159-162, (1994) · Zbl 0796.93026
[7] Li, H., Niculescu, S.-I., Dugard, L., & Dion, J.-M. (1996). Robust H∞ control for uncertain linear time-delay systems: A linear matrix inequality approach. Part I. Proceedings of the 35th IEEE conference decision and control, Kobe, Japan.
[8] Niculescu, S.-I. (1997). Time-delay systems: Qualitative aspects on stability and stabilization (in French). Paris: Diderot Multimedia.
[9] Niculescu, S.-I., de Souza, C. E., Dion, J.-M., & Dugard, L. (1995). Robust H∞ memoryless control for uncertain linear systems with time-varying delay. Proceedings of the third European control conference, Rome, Italy (pp. 1814-1818).
[10] Răsvan, V. (1983). Absolute stability of time-delay control systems (in Russian). Moscow: Nauka.
[11] Shen, J.C.; Chen, B.S.; Kung, F.C., Memoryless stabilization of uncertain dynamic delay systems: Riccati equation approach, IEEE transactions on automatic control, 36, 638-640, (1991)
[12] Xie, L., & de Souza, C. E. (1993). Robust stabilization and disturbance attenuation for uncertain delay systems. Proceedings of the second European control conference, Groningen, The Netherlands (pp. 667-672).
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