Technical communique: Reciprocally convex approach to stability of systems with time-varying delays

  • Authors:

  • PooGyeon Park;Jeong Wan Ko;Changki Jeong

  • Affiliations:

  • Division of IT Convergence Engineering, Pohang University of Science and Technology, Pohang, Republic of Korea and Electronic and Electrical Engineering, Pohang University of Science and Technolog ...;Electronic and Electrical Engineering, Pohang University of Science and Technology, Pohang, Republic of Korea;Electronic and Electrical Engineering, Pohang University of Science and Technology, Pohang, Republic of Korea

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2011

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Abstract

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.