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Article

New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay †

by 1,2,* and 3,4
1
Higher Institute of Applied Sciences and Technology University of Gafsa, Gafsa 2112, Tunisia
2
SYS’COM Laboratory, National Engineering School of Tunis (ENIT), Belvedere 1002, Tunisia
3
Department of Computer Engineering, College of Computers and Information Technology, Taif University, Taif 888, Saudi Arabia
4
LARA Laboratory, National Engineering School of Tunis (ENIT), University of Tunis ElManar, Belvedere 1002, Tunisia
*
Author to whom correspondence should be addressed.
This work is part of a Tunisian-South African cooperation scientific research project. In this context, we thank the Ministry of Higher Education and Scientific Research of Tunisia and the SYS’COM laboratory that has supported this research.
Mathematics 2020, 8(9), 1531; https://doi.org/10.3390/math8091531
Received: 1 August 2020 / Revised: 24 August 2020 / Accepted: 31 August 2020 / Published: 8 September 2020
(This article belongs to the Special Issue Advances in Study of Time-Delay Systems and Their Applications)
In this paper, the stability problem of discrete time delay systems is investigated. The class of systems under consideration is represented by delayed difference equations and models nonlinear discrete time systems with time varying delay. It is transformed into an arrow from matrix representation which allows the use of aggregation techniques and M-matrix properties to determine novel sufficient stability conditions. 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 nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Next, it is shown how to use our method in designing a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. Finally, several examples are provided to show the effectiveness of the introduced technique. View Full-Text
Keywords: nonlinear discrete time systems; time varying delay; delay dependent stability; M-matrix; Lure Postnikov systems nonlinear discrete time systems; time varying delay; delay dependent stability; M-matrix; Lure Postnikov systems
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MDPI and ACS Style

Elmadssia, S.; Saadaoui, K. New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay. Mathematics 2020, 8, 1531. https://doi.org/10.3390/math8091531

AMA Style

Elmadssia S, Saadaoui K. New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay. Mathematics. 2020; 8(9):1531. https://doi.org/10.3390/math8091531

Chicago/Turabian Style

Elmadssia, Sami, and Karim Saadaoui. 2020. "New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay" Mathematics 8, no. 9: 1531. https://doi.org/10.3390/math8091531

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