zbMATH — the first resource for mathematics

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).

MSC:
 93D10 Popov-type stability of feedback systems 93C23 Control/observation systems governed by functional-differential equations
Full Text:
References:
 [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).
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.