Acta mathematica scientia,Series A ›› 2001, Vol. 21 ›› Issue (3): 416-423.
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TUN Shu-Jin, ZHANG Shu-Nian
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国家自然科学基金资助项目（Ｎｏ．１９８３１０３０）
Abstract:
首先引入了时滞差分系统基于两种测度的极端稳定性概念，然后建立了一些关于时滞差分系统（犺０，犺）极端稳定性（极端一致稳定性，极端渐近稳定性，极端一致渐近稳定性）的判定准则．在所得到的定理中，对Δ犞的限制较弱，特别地，Δ犞甚至可以恒为正，从而便于实际应用．
Key words: 时滞差分系统, 基于两种测度的极端稳定性, Ｌｉａｐｕｎｏｖ函数．
CLC Number:
TUN Shu-Jin, ZHANG Shu-Nian. Extreme Stability in Terms of Two Measures for Difference Systems with Finite Delay[J].Acta mathematica scientia,Series A, 2001, 21(3): 416-423.
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１ ＳｈｕｎｉａｎＺｈａｎｇ．Ａｎｉｍｐｒｏｖｅｍｅｎｔｉｎｓｔａｂｉｌｉｔｙｏｆｄｅｌａｙｄｉｆｆｅｒｅｎｃｅｓｙｓｔｅｍｓ．ＣｈｉｎｅｓｅＳｃｉｅｎｃｅＢｕｌｌｅｔｉｎ，１９９８，４３：５４４－５４７ ２ ＬｉｕＸ，ＦｕＸ．Ｓｔａｂｉｌｉｔｙｃｒｉｔｅｒｉａｉｎｔｅｒｍｓｏｆｔｗｏｍｅａｓｕｒｅｓｆｏｒｄｉｓｃｒｅｔｅｓｙｓｔｅｍｓ．ＣｏｍｐｕｔｅｒＭａｔｈＡｐｐｌｉｃ，１９９８，３６：３２７ －３３７ ３ Ｌａｋｓｈｍｉｋａｎｔｈａｍ Ｖ，ＸｉｎｚｈｉＬｉｕ．Ｓｔａｂｉｌｉｔｙｃｒｉｔｅｒｉａｆｏｒｉｍｐｕｌｓｉｖｅｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｉｎｔｅｒｍｓｏｆｔｗｏｍｅａｓｕｒｅｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９８９，１３７：５９１－６０４ ４ ＸｉｎｚｈｉＬｉｕ．Ｓｔａｂｉｌｉｔｙｉｎｔｅｒｍｓｏｆｔｗｏｍｅａｓｕｒｅｓｆｏｒｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．ＤｉｆｆｅｒｅｎｔｉａｌａｎｄＩｎｔｅｇｒａｌＥｑｕａｔｉｏｎｓ，１９８９，１：１３－２１ ５ ＸｉｎｚｈｉＬｉｕ．ＰｅｒｔｕｒｂｉｎｇｆａｍｉｌｉｅｓｏｆＬｙａｐｕｎｏｖｆｕｎｃｔｉｏｎｓａｎｄａｓｙｍｐｔｏｔｉｃｓｔａｂｉｌｉｔｙ．ＡｐｐｌＭａｔｈＰｈｙＳｃｉ，１９８９，２３：２３－３４ ６ ＬａＳａｌｌｅＪＰ．Ａｓｔｕｄｙｏｆｓｙｎｃｈｒｏｎｏｕｓａｓｙｍｐｔｏｔｉｃｓｔａｂｉｌｉｔｙ．ＡｎｎｏｆＭａｔｈ，１９５７，６５：５７１－５８１ ７ ＴａｒｏＹｏｓｈｉｚａｗａ．ＳｔａｂｉｌｉｔｙｔｈｅｏｒｙｂｙＬｉａｐｕｎｏｖ＇ｓｓｅｃｏｎｄｍｅｔｈｏｄ．ＴｈｅｍａｔｈｅｍａｔｉｃａｌｓｏｃｉｅｔｙｏｆＪａｐｅｎ，１９６６．６４－７２ ８ 廖晓昕．稳定性的理论、方法和应用．武汉：华中理工大学出版社，１９９９．１２－１３
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