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Reciprocally convex approach to stability of systems with time-varying delays. (English) Zbl 1209.93076
Summary: Whereas the upper bound lemma for matrix cross-product, introduced by Park (1999) and modified by {\it Y. S. Moon, P. Park, W. H. Kwon} and {\it 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.

93C30Control systems governed by other functional relations
93D20Asymptotic stability of control systems
93D99Stability of control systems
Full Text: DOI
[1] Fridman, E.; Shaked, U.: Delay-dependent stability and H$\infty $ control: constant and time-varying delays, International journal of control 76, No. 1, 48-60 (2003) · Zbl 1023.93032 · doi:10.1080/0020717021000049151
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[6] Moon, Y. S.; Park, P.; Kwon, W. H.; Lee, Y. S.: Delay-dependent robust stabilization of uncertain state-delayed systems, International journal of control 74, No. 14, 1447-1455 (2001) · Zbl 1023.93055 · doi:10.1080/00207170110067116
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[8] Park, P.; Ko, J. W.: Stability and robust stability for systems with a time-varying delay, Automatica 43, No. 10, 1855-1858 (2007) · Zbl 1120.93043 · doi:10.1016/j.automatica.2007.02.022
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[10] Wu, M.; Feng, Z. -Y.; He, Y.: Improved delay-dependent absolute stability of Lur’e systems with time-delay, International journal of control, automation, and systems 7, No. 6, 1009-1014 (2009)
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