Discrete inequalities based on multiple auxiliary functions and their applications to stability analysis of time-delay systems

摘要

This paper presents new discrete inequalities for single summation and double summation. These inequalities are based on multiple auxiliary functions and include the Jensen discrete inequality and the discrete Wirtinger-based inequality as special cases. An application of these discrete inequalities to analyze stability of linear discrete systems with an interval time-varying delay is studied and a less conservative stability condition is obtained. Three numerical examples are given to show the effectiveness of the obtained stability condition. (C) 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.