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

Kun Liu, Emilia Fridman, Karl Henrik Johansson, Yuanqing Xia

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)222-231
Number of pages10
JournalAutomatica
Volume69
DOIs
StatePublished - 1 Jul 2016

Keywords

  • Gamma-distributed delays
  • Lyapunov method
  • New integral and summation inequalities
  • Poisson-distributed delays

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