A Liapunov functional for a scalar differential difference equation
E. F. Infante, J. A. Walker
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Source: Crossref
Published: Jan 1, 1978
DOI: 10.1017/s030821050001982x
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Synopsis Given the scalar, retarded differential difference equation x '( t )= ax ( t ) + bx ( t −τ), a quadratic functional in explicit form is obtained that yields necessary and sufficient conditions for the asymptotic stability of this equation. This functional a Liapunov functional, is obtained through the study of the Liapunov functions associated with a difference equation approximation of the difference differential equation. The functional then obtained not only yields necessary and sufficient conditions for asymptotic stability, but provides estimates for rates of decay of the solutions as well as conditions, for asymptotic stability independent of the magnitude of the delay τ.
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