2016/02/17 by Kun Liu, Liu, Kun, Emilia Fridman +5
Engineering · Mathematics · #FOS: Electrical engineering #Nonlinear Differential Equations Analysis #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1602.05281
openalex publication_date 2016/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 thanks to the introduced generalized inequalities are demonstrated by examples.