A combined first- and second-order reciprocal convexity approach for stability analysis of systems with interval time-varying delays. Issue 9 (June 2016)

• Record Type: Journal Article
• Authors: Lee, Won Il; Lee, Seok Young; Park, PooGyeon
• Is Part Of: Journal of the Franklin Institute. Volume 353:Issue 9(2016:Jun.)
• Page Start: 2104
• Page End: 2116
• Publication Date: 2016-06
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2016.03.017
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: For the interval time-varying delay systems, Jensen inequality lemma yields some terms with the inverse of convex and squared convex parameters, which often makes it difficult to find their bounds. Recently, reciprocal and second-order reciprocal convexity approaches have been proposed to handle the difficulties with a set of convex parameters and a set of squared convex parameters, respectively, but these approaches do not investigate the relation between the two sets. This paper offers much tighter bounds of those terms utilizing the relations among the two sets with the lower bound lemma. Based on the new approach and Lyapunov theory, less conservative stability criteria for time delay systems are developed. To show the effectiveness of the new approach, two numerical examples are given.