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

Sami Elmadssia and Karim Saadaoui
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Sami Elmadssia: Higher Institute of Applied Sciences and Technology University of Gafsa, Gafsa 2112, Tunisia
Karim Saadaoui: Department of Computer Engineering, College of Computers and Information Technology, Taif University, Taif 888, Saudi Arabia

Mathematics, 2020, vol. 8, issue 9, 1-19

Abstract: 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.

Keywords: nonlinear discrete time systems; time varying delay; delay dependent stability; M-matrix; Lure Postnikov systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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