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- W4313442360 abstract "Many real phenomena can be modeled by linear delayed systems. One of the most important problems for such systems is the asymptotic stability of the solutions, the general theory of which has been developed in the books of Hale [1], Bellman and Cook [2] and Burton [3]. It is known that a linear system with time delays is asymptotically stable if undelayed negative feedbacks dominate delayed interactions [6, 7]. When there are time delays in negative feedbacks it is natural to expect that the system remains asymptotically stable if these delays are sufficiently small and the delayed negative feedbacks dominate delayed interactions. If this is the case, then one can ignore the effect of small delays in the negative feedbacks when they are dominant. The object of this note is to give an affirmative answer to the above question. By adopting the technique of degenerate Liapunov functionals [5], we show that systems without instantaneous dissipative terms are asymptotically stable if they are diagonally dominant and the delays in the diagonal are short enough." @default.
- W4313442360 created "2023-01-06" @default.
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- W4313442360 date "2023-01-03" @default.
- W4313442360 modified "2023-09-23" @default.
- W4313442360 title "Asymptotic Stability of Linear Delayed Systems without Instantaneous Dissipative Terms*" @default.
- W4313442360 doi "https://doi.org/10.1201/9781315136875-15" @default.
- W4313442360 hasPublicationYear "2023" @default.
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