Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay

Zhang, Chuan-Ke, He, Yong, Jiang, Lin ORCID: 0000-0001-6531-2791, Wu, Min and Zeng, Hong-Bing (2017) Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 62 (5). pp. 2582-2588. ISSN 0018-9286, 1558-2523

Text Technical Note 15-1603 2016 IEEE TAC.pdf - Author Accepted Manuscript Download (114kB)

Abstract

Summation inequality is an important technique for analysis of discrete-time systems with a time-varying delay. It seems that from the literature a tighter inequality usually leads to a less conservative criterion. Based on H performance analysis problem, this note presents different findings on the relationship between the conservatism of bounded real lemma (BRL) and the tightness of summation inequality. Firstly, the BRL obtained by the Wirtinger-based inequality (WBI) is not always less conservative than the one by the Jensen-based inequality although the WBI is tighter. Secondly, the WBI is tighter than a general free-matrix-based inequality (GFMBI) developed in this note, while the BRL obtained via the GFMBI is less conservative than the WBI-based BRL. Finally, a numerical example is given to demonstrate those findings.

Item Type:	Article
Uncontrolled Keywords:	Discrete-time system, time-varying delay, summation inequality, bounded real lemma
Depositing User:	Symplectic Admin
Date Deposited:	12 Aug 2016 08:34
Last Modified:	23 May 2026 00:18
DOI:	10.1109/TAC.2016.2600024
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3002905
Disclaimer:	The University of Liverpool is not responsible for content contained on other websites from links within repository metadata. Please contact us if you notice anything that appears incorrect or inappropriate.