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A discrete delay decomposition approach to stability of linear retarded and neutral systems

journal contribution
posted on 06.12.2017, 00:00 authored by Qing-Long HanQing-Long Han
This paper is concerned with stability of linear time-delay systems of both retarded and neutral types by using some new simple quadratic Lyapunov-Krasovskii functionals. These Lyapunov-Krasovskii functionals consist of two parts. One part comes from some existing Lyapunov-Krasovskii functionals employed in [Han, Q.-L. (2005a). Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica, 41, 2171-2176; Han, Q.-L. (2005b). A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices. International Journal of Systems Science, 36, 469-475]. The other part is constructed by uniformly dividing the discrete delay interval into multiple segments and choosing proper functionals with different weighted matrices corresponding to different segments. Then using these new simple quadratic Lyapunov-Krasovskii functionals, some new discrete delay-dependent stability criteria are derived for both retarded systems and neutral systems. It is shown that these criteria for retarded systems and neutral systems are always less conservative than the ones in Han (2005a) and Han (2005b) cited above, respectively. Numerical examples also show that the results obtained in this paper significantly improve the estimate of the discrete delay limit for stability over some other existing results.

Funding

Category 1 - Australian Competitive Grants (this includes ARC, NHMRC)

History

Volume

45

Issue

2

Start Page

517

End Page

524

Number of Pages

8

ISSN

0005-1098

Location

Oxford, United Kingdom

Publisher

Elsevier Ltd

Language

en-aus

Peer Reviewed

Yes

Open Access

No

External Author Affiliations

Centre for Intelligent and Networked Systems (CINS); Institute for Resource Industries and Sustainability (IRIS);

Era Eligible

Yes

Journal

Automatica.