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delay system; time-varying delay; instability

References:

[1] Chen J., Gu, G., Nett C. N.: **A new method for computing delay margins for stability of linear delay systems**. Systems Control Lett. 26 (1995), 107–117 DOI 10.1016/0167-6911(94)00111-8 | MR 1349541 | Zbl 0877.93117

[2] Cooke K. L.: **Linear functional differential equations of asymptotically autonomous type**. J. Differential Equations 7 (1970), 154–174 DOI 10.1016/0022-0396(70)90130-0 | MR 0255944 | Zbl 0185.18001

[3] Cooke K. L., Wiener J.: **A survey of differential equations with piecewise continuous arguments**. In: Delay Differential Equations and Dynamical Systems (S. Busenberg and M. Martelli, eds., Lecture Notes in Mathematics 1475), Springer–Verlag, Berlin – Heidelberg 1991, pp. 1–15 MR 1132014 | Zbl 0737.34045

[4] Datko R.: **Lyapunov functionals for certain linear delay–differential equations in a Hilbert space**. J. Math. Anal. Appl. 76 (1980), 37–57 DOI 10.1016/0022-247X(80)90057-8 | MR 0586642 | Zbl 0482.34055

[5] Hale J. K., Lunel S. M. V.: **Introduction to Functional Differential Equations**. Springer–Verlag, New York 1993 MR 1243878 | Zbl 0787.34002

[6] Infante E. F., Castelan W. B.: **A Lyapunov functional for a matrix difference–differential equation**. J. Differential Equations 29 (1978), 439–451 DOI 10.1016/0022-0396(78)90051-7 | MR 0507489

[7] Kojima A., Uchida, K., Shimemura E.: **Robust stabilization of uncertain time delay systems via combined internal – external approach**. IEEE Trans. Automat. Control 38 (1993), 373–378 DOI 10.1109/9.250497 | MR 1206835 | Zbl 0773.93066

[8] (ed.) W. Levine: **The Control Handbook**. CRC Press, Boca Raton 1996 Zbl 1214.93001

[9] Louisell J.: **Instability and quenching in delay systems having constant coefficients and time-varying delays**. J. Math. Anal. Appl. Submitted

[10] Louisell J.: **New examples of quenching in delay differential equations having time-varying delay**. In: Proc. 5th European Control Conference, F 1023–1, Karlsruhe 1999

[11] Louisell J.: **Numerics of the stability exponent and eigenvalue abscissas of a matrix delay system**. In: Stability and Control of Time–Delay Systems (L. Dugard and E. I. Verriest, eds., Lecture Notes in Control and Information Sciences 228), Springer–Verlag, Berlin – Heidelberg – New York 1997, pp. 140–157 MR 1482576

[12] Louisell J.: **Growth estimates and asymptotic stability for a class of differential-delay equation having time-varying delay**. J. Math. Anal. Appl. 164 (1992), 453–479 DOI 10.1016/0022-247X(92)90127-Y | MR 1151047 | Zbl 0755.34071

[13] Louisell J.: **A stability analysis for a class of differential-delay equation having time-varying delay**. In: Delay Differential Equations and Dynamical Systems (S. Busenberg and M. Martelli, eds., Lecture Notes in Mathematics 1475), Springer–Verlag, Berlin – Heidelberg 1991, pp. 225–242 MR 1132034

[14] Markus L., Yamabe H.: **Global stability criteria for differential systems**. Osaka J. Math. 12 (1960), 305–317 MR 0126019 | Zbl 0096.28802

[15] Marshall J. E., Gorecki H., Walton, K., Korytowski A.: **Time–Delay Systems: Stability and Performance Criteria with Applications**. Ellis Horwood, New York 1992 Zbl 0769.93001

[16] Niculescu S.-I.: **Stability and hyperbolicity of linear systems with delayed state: a matrix–pencil approach**. IMA J. Math. Control Inform. 15 (1998), 331–347 DOI 10.1093/imamci/15.4.331 | MR 1663488

[17] Niculescu S.-I., Souza C. E. de, Dugard, L., Dion J.-M.: **Robust exponential stability of uncertain systems with time–varying delays**. IEEE Trans. Automat. Control 43 (1998), 743–748 DOI 10.1109/9.668851 | MR 1618039 | Zbl 0912.93053

[18] Repin I. M.: **Quadratic Liapunov functionals for systems with delays**. Prikl. Mat. Mekh. 29 (1965), 564–566 MR 0206422

[19] Sun Y.-J., Hsieh J.-G., Yang H.-C.: **On the stability of uncertain systems with multiple time–varying delays**. IEEE Trans. Automat. Control 42 (1997), 101–105 DOI 10.1109/9.553692 | MR 1439369 | Zbl 0871.93045

[20] Verriest E. I.: **Robust stability of time varying systems with unknown bounded delays**. In: Proc. 33rd IEEE Conference Decision and Control, Lake Buena Vista 1994, pp. 417–422