Journal
AUTOMATICA
Volume 47, Issue 1, Pages 235-238Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2010.10.014
Keywords
Reciprocally convex combination; Delay systems; Stability
Funding
- MKE (The Ministry of Knowledge Economy), Korea [NIPA-2010-(C1090-1021-0006), NIPA-2010-(C1090-1011-0011)]
- Ministry of Education, Science and Technology [R31-2008-000-10100-0]
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Whereas the upper bound lemma for matrix cross-product, introduced by Park (1999) and modified by Moon, Park, Kwon, and Lee (2001), plays a key role in guiding various delay-dependent criteria for delayed systems, the Jensen 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 the Jensen inequality lemma. (C) 2010 Elsevier Ltd. All rights reserved.
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