Stability in linear delay equations. (English) Zbl 0569.34061
For linear autonomous differential difference equations of retarded or neutral type, necessary and sufficient conditions are given for the zero solution to be stable (hyperbolic) for all value of the delays.
MSC:
| 34K20 | Stability theory of functional-differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
References:
| [1] | Avellar, C. E.; Hale, J. K., On the zeros of exponential polynomials, J. Math. Anal. Appl., 73, 434-452 (1980) · Zbl 0435.30005 |
| [2] | Cooke, K. L.; Ferreira, J., Stability conditions for linear retarded functional differential equations, J. Math. Anal. Appl., 96, 480-504 (1983) · Zbl 0526.34057 |
| [3] | Datko, R., A procedure for determination of the exponential stability of certain differential difference equations, Quart. Appl. Math., 36, 279-292 (1978) · Zbl 0405.34051 |
| [4] | Hale, J. K., Functional Differential Equations (1977), Springer-Verlag: Springer-Verlag New York/Berlin · Zbl 0425.34048 |
| [5] | Repin, Yu. M., On conditions for the stability of systems of differential equations for arbitrary delays, Uchen. Zap. Ural., 23, 31-34 (1960) |
| [6] | Silkowskii, R., A star shaped condition for stability of linear retarded functional differential equations, (Proc. Roy. Soc. Edinburgh Ser. A, 83 (1979)), 189-198 · Zbl 0417.34110 |
| [7] | Zivotovskii, L. A., Absolute stability for the solutions of differential equations with retarded arguments, (Trudy Sem. Diff. Urav. Otkly. Arg., 7 (1969)), 82-91 |
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