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 Y. S. Moon, P. Park, W. H. Kwon and 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.


93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93D20 Asymptotic stability in control theory
93D99 Stability of control systems


Zbl 1023.93055
Full Text: DOI


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