Abstract
This paper deals with the problem of global exponential stability for a discrete-time Rayleigh system with delays. By using the mathematical induction method, some sufficient conditions are proposed for the global exponential stability of the discrete-time Rayleigh system. Finally, a numerical example is given to illustrate the effectiveness and application of the obtained results.
Highlights
In recent years, Rayleigh system has been widely investigated, due to its broad applications in physics, neural networks, electronics, engineering technique and mechanics, and other fields. e numerical solutions of Rayleigh equation for the scattering of electromagnetic waves from rough dielectric films on perfectly conducting substrates were studied by Madrazo and Maradudin [1]
For the dynamic behavior analysis of delayed dynamic systems, different types of time delays have been taken into account by using a variety of methods that include linear matrix inequality (LMI) approach, M-matrix theory, topological degree theory, and Lyapunov functional method, see e.g., [13,14,15,16]. e stability problem of the Rayleigh system with delays is an important issue from both theoretical and practical points of view, which has been extensively studied by many authors
Raja and Marshal Anthoni [28] dealt with the problem of stability analysis for a class of discrete-time BAM neural networks with time-varying delays by employing the Lyapunov functional and linear matrix inequality (LMI) approach
Summary
Rayleigh system has been widely investigated, due to its broad applications in physics, neural networks, electronics, engineering technique and mechanics, and other fields. e numerical solutions of Rayleigh equation for the scattering of electromagnetic waves from rough dielectric films on perfectly conducting substrates were studied by Madrazo and Maradudin [1]. In [6], the authors dealt with the existence of asymptotically stable periodic solutions of a Rayleigh-type equation. Cao and Wan [17] considered stability and synchronization of an inertial BAM neural network with time delays. To the best of our knowledge, there are few results involving a discrete-time Rayleigh system with delays till now. We derive a discrete-time Rayleigh system by the difference method. Some sufficient conditions are obtained for global exponential stability of a discretetime Rayleigh system with delays by using the mathematical induction method. (1) We derive a new discrete-time Rayleigh system with delays by using the difference method. (3) We use the mathematical induction method for obtaining global exponential stability condition in this paper which is easier than the traditional Lyapunov functional method and linear matrix inequality method. Denote [a, b]Z {a, a + 1, . . . , b − 1, b} for a, b ∈ Z and a ≤ b
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