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.
Highlights
The class of nonlinear delay systems studied in this manuscript are governed by the following difference equation:
In this sub-section, system S1 with time varying delay which satisfies the below condition: h1 ≤ h ( k ) ≤ h2, (25)
The model consists of a static nonlinearity in cascade with a dynamic linear time delay system
Summary
Stability of delay systems has been examined intensively by the academics from the control community [1,2,3,4,5,6,7,8,9,10,11,12,13], because several physical systems, like networked control systems, biological systems and chemical systems, are generally associated with time delays, [14,15,16,17,18,19]. We show 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 [24,25,26,27,28,29,30,31] Note that this system is one of the most important classes of nonlinear control systems and remains one of the main problems in control theory which is intensively examined due to its various practical applications [32,33,34,35,36,37,38].
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