## 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.

### MSC:

 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

### Keywords:

reciprocally convex combination; delay systems; stability

Zbl 1023.93055
Full Text:

### References:

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