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Stabilizing a class of time delay systems using the Hermite–Biehler theorem. (English) Zbl 1109.93363
The paper contains the applicable form of a Hermite-Biehler type theorem for the quasi-polynomial $f(s) = \sum_{j=1}^{n}\exp(\lambda_{j}s)P_{j}(s)$ $$\lambda_{j}$$ being some real numbers.

##### MSC:
 93D15 Stabilization of systems by feedback 93C23 Control/observation systems governed by functional-differential equations
##### Keywords:
linear delay systems; stability; quasi-polynomials
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##### References:
 [1] Bhattacharyya, S.P.; Chapellat, H.; Keel, L.H., Robust control: the parametric approach, (1995), Prentice-Hall Englewood Cliffs, NJ · Zbl 0838.93008 [2] A. Bülent Özguler, A. Aydn Koçan, An Analytic Determination of Stabilizing Feedback Gains, Report Nr. 321, Institutfür Dynamische Systeme, Universität Bremen, 1994 [3] Ho, M.T.; Datta, A.; Bhattacharyya, S.P., Generalizations of the hermite – biehler theorem, Linear algebra appl., 302-303, 135-153, (1999) · Zbl 0949.15037 [4] Pontryagin, L.S., On the zeros of some elementary transcendental functions, English translation, Amer. math. soc., 2, 95-110, (1955) · Zbl 0068.05803 [5] () [6] Bellman, R.; Cooks, K.L., Differential-difference equations, (1963), Academic Press Inc London [7] Kharitonov, V.L.; Zhabko, A.P., Robust stability of time delay systems, IEEE trans. automat. contr., 39, 12, 2388-2397, (1994) · Zbl 0811.93042 [8] G.J. Silva, A. Datta, S.P. Bhattacharyya, Stabilization of Time Delay Systems, American Control Conference 2000, pp. 963-970 [9] M.T. Ho, A. Datta, S.P. Bhattacharyya, A Linear Programming Characterization of all Stabilizing PID Controllers, American Control Conference 1997, pp. 3922-3928 [10] Gantmacher, F.R., The theory of matrices, (1959), Chelsea Publishing Company New York · Zbl 0085.01001
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