Generalized Jensen inequalities with application to stability analysis of systems with distributed delays over infinite time-horizons

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• 作者：Kun Liu^a ; ^{kunliubit@bit.edu.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Emilia Fridman^b ; ^{emilia@eng.tau.ac.il" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Karl Henrik Johansson^c ; ^{kallej@kth.se" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Yuanqing Xia^a ; ^{xia_yuanqing@bit.edu.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：New integral and summation inequalities ; Gamma-distributed delays ; Poisson-distributed delays ; Lyapunov method
• 刊名：Automatica
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：69
• 期：Complete
• 页码：222-231
• 全文大小：685 K

文摘

The Jensen inequality has been recognized as a powerful tool to deal with the stability of time-delay systems. Recently, a new inequality that encompasses the Jensen inequality was proposed for the stability analysis of systems with finite delays. In this paper, we first present a generalized integral inequality and its double integral extension. It is shown how these inequalities can be applied to improve the stability result for linear continuous-time systems with gamma-distributed delays. Then, for the discrete-time counterpart we provide an extended Jensen summation inequality with infinite sequences, which leads to less conservative stability conditions for linear discrete-time systems with Poisson-distributed delays. The improvements obtained by the introduced generalized inequalities are demonstrated through examples.