New stability conditions for class of nonlinear discrete-time systems with time-varying delay
preprintposted on 2021-03-09, 17:59 authored by SAMI ELMADSSIASAMI ELMADSSIA, KARIM SADAAOUI
The problem of stability analysis for a class of nonlinear discrete time systems with time varying delay is studied in this work. Such systems are modeled by delayed difference equations. Subsequently, this system is transformed into an arrow form matrix representation. Using M-matrix properties, novel sufficient stability conditions are determined. It is shown how to use our method to design a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of a nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Several examples are provided to show the effectiveness of the introduced technique.
This work is part of a Tunisian-South African cooperation scientific research project. We thank the Ministry of Higher Education and Scientific Research of Tunisia that has supported this research. Qing-Guo WANG acknowledges the financial support of the National Research Foundation of South Africa (Grant Numbers: 113340, 120106), which partially funded his research on this work.
Email Address of Submitting Authorsami.email@example.com
ORCID of Submitting Authorhttps://orcid.org/0000-0003-1057-2929
Submitting Author's InstitutionNational Engineering School of Tunis
Submitting Author's CountryTunisia
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