Stability and control of feedback systems with time delays. (English) Zbl 1052.93028

Summary: Feedback systems are important in applications, e.g. optical feedback lasers, phase-locked frequency synthesizers and wave equations with feedback stabilization at the boundary, and the problem regarding sensitivity and robustness of the feedback system with respect to time delays has attracted much attention. This paper continues the discussion on sensitivity and robustness of the feedback stabilization of neutral differential delay equations with respect to variation in the delays and with respect to a time delay in the feedback loop. The main result shows that robustness of the stabilization actually depends on the radius of the essential spectrum of the semigroup associated with the equation.


93C23 Control/observation systems governed by functional-differential equations
93D20 Asymptotic stability in control theory
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[1] DOI: 10.1137/0514007 · Zbl 0528.34062
[2] Corduneanu C., Almost Periodic Functions (1968) · Zbl 0175.09101
[3] Hale J. K., An Introduction to Functional Differential Equations (1993) · Zbl 0787.34002
[4] Hale J. K. Verduyn Lunel S. M. 2001Effects of small delays on stability and controlIn H. Bart, I. Gohberg and A.C.M. Ran, (eds)Operator Theory and Analysis(Birkhäuser) pp. 275–301 · Zbl 0983.34070
[5] DOI: 10.1093/imamci/19.1_and_2.5 · Zbl 1005.93026
[6] DOI: 10.1016/0022-0396(74)90089-8 · Zbl 0294.34047
[7] DOI: 10.2307/2154470 · Zbl 0768.34041
[8] Kato T., Perturbation Theory for Linear Operators (1980) · Zbl 0435.47001
[9] Levin B. J. A., Distribution of Zeros of Entire Function (1972)
[10] DOI: 10.1137/S0363012993250700 · Zbl 0853.93081
[11] DOI: 10.1007/BF01211750 · Zbl 0874.93077
[12] DOI: 10.1016/0167-6911(96)00002-3 · Zbl 0866.93089
[13] DOI: 10.1109/TAC.1983.1103286 · Zbl 0527.93049
[14] Pandolfi L., Bollettino UMI 12 pp 626– (1975)
[15] Salamon D., Control and Observation of Neutral Systems (1984) · Zbl 0546.93041
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