Generalized Jensen Inequalities with Application to Stability Analysis of Systems with Distributed Delays over Infinite Time-Horizons
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 thanks to the introduced generalized inequalities are demonstrated by examples.
Keywords
Cite
@article{arxiv.1602.05281,
title = {Generalized Jensen Inequalities with Application to Stability Analysis of Systems with Distributed Delays over Infinite Time-Horizons},
author = {Kun Liu and Emilia Fridman and Karl Henrik Johansson and Yuanqing Xia},
journal= {arXiv preprint arXiv:1602.05281},
year = {2016}
}
Comments
12 pages, 5 figures