An Extended Kalman-Yakubovich-Popov Lemma for Positive Systems∗. Issue 11 (2015)

• Record Type: Journal Article
• Authors: Rantzer, Anders
• Is Part Of: IFAC-PapersOnLine. Volume 48:Issue 11(2015)
• Page Start: 242
• Page End: 245
• Publication Date: 2015
• Subjects: Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2015.09.191
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: An extended Kalman-Yakubovich-Popov Lemma for positive systems is proved, which generalizes earlier versions in several respects: Non-strict inequalities are treated. Matrix assumptions are less restrictive. Moreover, a new equivalence is introduced in terms of linear programming rather than semi-definite programming. As a complement, we also prove that a symmetric Metzler matrix with m non-zero entries above the diagonal is negative semi-definite if and only if it can be written as a sum of m negative semi-definite matrices, each of which has only four non-zero entries.