A note on equivalence between two integral inequalities for time-delay systems

• Xiaofu Ji ^[1] ; Hongye Su ^[2]
  1. [1] Jiangsu University

     Jiangsu University

     China

     
  2. [2] University, Hangzhou, 310027, PR China
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 53, 2015, págs. 244-246
• Idioma: inglés
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• Resumen

  • Jensen’s inequality and extended Jensen’s inequality are two important integral inequalities when problems of stability analysis and controller synthesis for time-delay systems are considered. The extended Jensen’s inequality introduces two additional free matrices and is generally regarded to be less conservative than Jensen’s inequality. The equivalence between Jensen’s inequality and extended Jensen’s inequality in bounding the quadratic term in Lyapunov functional of time-delay systems is presented and theoretically proved. It is shown that the extended Jensen’s inequality does not decrease the lower bound of this quadratic term obtained using Jensen’s inequality, and then it does not reduce the conservativeness though two additional free matrices and are involved.