A general approach is developed for making a given stable discrete-time system chaotic via small-amplitude scalar-valued output feedback. Provided that the given nominal discrete-time system has an exponentially stable fixed point and has a well-defined relative degree at this fixed point with respect to a system parameter, a small-amplitude scalar-valued output-feedback can make the system chaotic within a neighborhood of the fixed point.
This technical note presents necessary and sufficient conditions for the stability and stabilization of fractional-order interval systems. The results are obtained in terms of linear matrix inequalities. Two illustrative examples are given to show that our results are effective and less conservative for checking the robust stability and designing the stabilizing controller for fractional-order interval systems.
No abstract is provided for this article.
This paper presents the design, simulation, hardware implementation and an application in liquid mixing of some hyperchaotic circuits, based on the digital signal processing (DSP) technology. The hyperchaotic Chen's system is used as an example to show the system discretization and variable renormalization in the design process. Numerical simulation is given to verify the hardware signal generator. The implemented hardware of Chen's system generates outputs in good agreement with the numerical simulation. The hyperchaotic signal output from the DSP is applied to generate complex perturbations in liquid mixing experiments. Dye dispersion experiments show that the induced hyperchaotic motion effectively helps enhance the mixing homogeneity in the stirred‐tank‐based mixer in our laboratory. Copyright © 2008 John Wiley & Sons, Ltd.
No abstract is provided for this article.
Cooperative diversity has been recently proposed as a way to form virtual antenna arrays and thereby mitigate the deleterious effect of fading channels in transmission. In an environment where multiple relays are available, selection of a subset of such relays may be required as, for example, in distributed space-time coding. In this study, the authors therefore use local measurements of the instantaneous channel conditions to select the best relay pair from a set of N available relays, which both come from the same cluster or different clusters, and then use these best relays for cooperation between the source and the destination. The authors also show that the best relay pair selection scheme has robustness against feedback error and outperforms a scheme based on selecting only the best single relay. The authors obtain analytical expressions for the probability density function, cumulative density function and the moment generating function of the received signal-to-noise ratio to derive closed-form expressions for outage probability over Rayleigh frequency flat-fading channels. The analytical results are supported by simulation studies.
No abstract is provided for this article.
A new approach to real-time digital secure speech communication is proposed based on the inversion theory of nonlinear discrete-time dynamical systems. The proposed approach uses an observable minimal-phase nonlinear discrete-time dynamical system, particularly with chaotic zero-dynamics, as the drive system to generate encrypted message signals for transmission. The receiver is the minimal left-inverse system of the drive system with the capability of synchronization. The receiver decrypts the received signal, recovers the original message in real-time. The effectiveness of the proposed approach and design is demonstrated via several examples for secure speech signals transmission. Performance evaluation of the designed secure communication system is discussed. Both analysis and simulation show that the new scheme is secure, simple, accurate and robust.
Some basic dynamical behaviors and the compound structure of a new four-dimensional autonomous chaotic system with cubic nonlinearities are investigated. A four-wing chaotic attractor is observed numerically. This attractor, however, is shown to be an numerical artifact by further theoretical analysis and analog circuit experiment. The observed four-wing attractor actually has two coexisting (upper and lower) attractors, which appear simultaneously and are located arbitrarily closely in the phase space. By introducing a simple linear state-feedback control term, some symmetries of the system and similarities of the linearized characteristics can be destroyed, thereby leading to the appearance of some diagonal and anti-diagonal periodic orbits, through which the upper and lower attractors can indeed be merged together to form a truly single four-wing chaotic attractor. This four-wing attractor is real; it is further confirmed analytically, numerically, as well as electronically in the paper. Moreover, by introducing a sign-switching control function, the system orbit can be manipulated so as to switch between two equilibria or among four equilibria, generating two one-side double-wing attractors, which can also be merged to yield a real four-wing attractor.
In this paper, we propose a new type of complex-valued memristor-based neural networks with time-varying delays and discuss their exponential stability. Firstly, by using a matrix measure method, the Halanay inequality and some analytic techniques, we derive a sufficient condition for the global exponential stability of this type of neural networks. Then, we build a Lyapunov functional and utilize the Halanay inequality to establish several criteria for the exponential stability of such networks with time-varying delays. Finally, we show two numerical simulations to demonstrate the theoretical results.