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中文摘要：
针对一般滞后型动态系统，本文建立了一种新型的充分必要指数稳定性定理以及新的稳定性分析方法，进一步扩展了李雅普诺夫函数的概念．初步地探讨了将新方法用于多时变时滞线性系统和线性定常系统的稳定性分析．和文献中已有的结果不同，所建立的稳定性判据不依赖于时变时滞的变化率．因此，所提方法适合具有非常快变的时变时滞的系统．文中也指出了进一步改进应用结果的研究方向．
英文摘要：
A new-type necessary and sufficient exponential stability theorem for general retarded dynamical systems, together with new stability analysis techniques is established, the concept of Lyapunov function is further extended. Linear systems with multiple time-varying delays and linear time-invariant systems are considered to show the applications of the new stability theorem and the new stability analysis techniques. Unlike some results in the literature, all of the established results do not depend on the derivatives of the time-varying delays. Therefore, the results are suitable to the cases with very fast time-varying delays. In addition, the research direction for improving the obtained results for linear systems with multiple time-varying delays has been also pointed out.
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