an:05862595
Zbl 1209.93076
Park, PooGyeon; Ko, Jeong Wan; Jeong, Changki
Reciprocally convex approach to stability of systems with time-varying delays
EN
Automatica 47, No. 1, 235-238 (2011).
00273378
2011
j
93C30 93D20 93D99
reciprocally convex combination; delay systems; stability
Summary: Whereas the upper bound lemma for matrix cross-product, introduced by Park (1999) and modified by \textit{Y. S. Moon, P. Park, W. H. Kwon} and \textit{Y. S. Lee} [Int. J. Control 74, No.~14, 1447--1455 (2001; Zbl 1023.93055)], plays a key role in guiding various delay-dependent criteria for delayed systems, Jensen's inequality has become an alternative as a way of reducing the number of decision variables. It directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities, resulting in a linear combination of positive functions weighted by the inverses of convex parameters. This paper suggests the lower bound lemma for such a combination, which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables, comparable to those based on Jensen's inequality lemma.
Zbl 1023.93055