Improved stability and performance for neutral systems with uncertain Markovian jump

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• 作者：Lianglin Xiongp>ap>p> ; p>p>bp>p> ; p>p>lianglin_5318@126.com" class="auth_mail" title="E-mail the corresponding authorp> ; Haiyang Zhangp>bp> ; Yongkun Lip>ap> ; Zixin Liup>cp>
• 关键词：Neutral Markovian jump systems ; Delay-dependent stabilization ; Partly unknown transition probability ; New integral inequality ; Linear matrix inequality (LMI)
• 刊名：Nonlinear Analysis: Hybrid Systems
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：19
• 期：Complete
• 页码：13-25
• 全文大小：426 K

文摘

This paper addresses the problem of the delay-dependent stability and pan id="mmlsi17" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1751570X15000485&_mathId=si17.gif&_user=111111111&_pii=S1751570X15000485&_rdoc=1&_issn=1751570X&md5=88e88c03cfde77f712c77aa54c62fe29" title="Click to view the MathML source">H∞pan>pan class="mathContainer hidden">pan class="mathCode">$H\infty$pan>pan>pan> performance for neutral systems with uncertain Markovian jump; the uncertainty of Markovian jump refers to the partial information on transition probability. In order to highlight the methods for the analysis of the systems, the neutral delay is assumed same as discrete delay. By the novel constructed Lyapunov functional, combining with the delay decomposition technique and free matrices, and using the new inequality rather than the Jensen inequality, the delay-dependent stability conditions are firstly obtained for the two kinds of neutral dynamical systems. Based on the stability condition, the pan id="mmlsi17" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1751570X15000485&_mathId=si17.gif&_user=111111111&_pii=S1751570X15000485&_rdoc=1&_issn=1751570X&md5=88e88c03cfde77f712c77aa54c62fe29" title="Click to view the MathML source">H∞pan>pan class="mathContainer hidden">pan class="mathCode">$H\infty$pan>pan>pan> performance result for the systems with Markovian jump is secondly provided. All of the delay-dependent stabilization results are formulated in terms of LMIs, which can be easily checked by the LMI control toolbox in Matlab. Finally, two numerical examples are given to show the validity and potential of the developed criteria.