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

• Kun Liu ^[1] ; Emilia Fridman ^[2] ; Karl Henrik Johansson ^[3] ; Yuanqing Xia ^[1]
  1. [1] Beijing Institute of Technology

     Beijing Institute of Technology

     China

     
  2. [2] Tel Aviv University

     Tel Aviv University

     Israel

     
  3. [3] Royal Institute of Technology

     Royal Institute of Technology

     Suecia

     

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• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 69, 2016, págs. 222-231
• Idioma: inglés
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• Resumen

  • 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.