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Stability of solutions of linear systems with retarded arguments


Author: John Abramowich
Journal: Proc. Amer. Math. Soc. 26 (1970), 60-64
MSC: Primary 34.75
DOI: https://doi.org/10.1090/S0002-9939-1970-0261118-0
MathSciNet review: 0261118
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Abstract: A criterion is given for the stability of the trivial solution of a linear system of differential equations with variable coefficients and variable delays under the assumptions of continuity and boundedness of the coefficients and continuous differentiability of the delays. The criterion is a condition on the roots of a certain ``quasi-polynomial,'' i.e. a polynomial in a variable and exponentials of that variable. The derivation is based on Lyapunov's direct method.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0261118-0
Keywords: Stability, linear differential system, variable coefficients, variable delays, quasi-polynomial, Lyapunov functional
Article copyright: © Copyright 1970 American Mathematical Society