Using fractional calculus, we analyze a classical switched-capacitor integrator when a fractional-order capacitor is employed in the feed-forward path. We show that using of a fractional-order capacitor, significantly large time constants can be realized with capacitances in the feedback path much smaller in value when compared with a conventional switched-capacitor integrator. Simulations and experimental results using a commercial super-capacitor with fractional-order characteristics confirmed via impedance spectroscopy are provided. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016

This paper investigates some basic concepts of fractional-order linear time invariant systems related to their physical and non-physical transfer functions, poles, stability, time domain, frequency domain, and their relationships for different fractional-order differential equations. The analytical formula that calculates the number of poles in physical and non-physical s-plane for different orders is achieved and verified using many practical examples. The stability contour versus the number of poles in the physical s-plane for different fractional-order systems is discussed in addition to

In this article a novel robust controller for the control of switched nonlinear systems with asynchronous switching is proposed considering state delays. The proposed approach improves the actual methodologies found in literature in which the disturbance rejection properties of these two methodologies consider a disturbance equal to zero but the proposed robust controller considers any kind of disturbances that makes this strategy to surpass other similar methodologies. The main objective is that the robust controller stabilizes the studied system in matched and unmatched modes considering the

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Over the last decades, synchronisation of chaotic systems has become an active research area and has been extensively and intensively studied due to the variety of important applications. Different types of chaos synchronisation have been presented, and many various methods and techniques for chaos synchronisation have been reported to investigate some types of chaos. In this paper, by combining full state hybrid projective synchronisation (FSHPS) and inverse full state hybrid projective synchronisation (IFSHPS), a new type of hybrid synchronisation between different dimensional incommensurate

In this paper, the problem of Q-S synchronisation for arbitrary dimensional chaotic dynamical systems in continuous-time is investigated. Based on nonlinear control method, we would like to present a constructive scheme to study the Q-S synchronisation between n-dimensional master chaotic system and m-dimensional slave chaotic system in arbitrary dimension. The new derived synchronisation result is proved using Lyapunov stability theory. In order to verify the effectiveness of the proposed method, our approach is applied to some typical chaotic systems and numerical simulations are given to

This paper proposes a novel generalized switched synchronization scheme among n fractional-order chaotic systems with various operatingmodes. Digital dynamic switches and dynamic scaling factors are employed, which offermany new capabilities. Dynamic switches determine the role of each system as a master or a slave. A system can either have a fixed role throughout the simulation time (static switching) or switch its role one or more times (dynamic switching). Dynamic scaling factors are used for each state variable of the master system. Such scaling factors control whether the master is a

The response of a commercial super-capacitor to an applied periodic current excitation in the form of a triangular waveform is investigated in this study. This waveform has a linear-with-time variation which enables linear charging and discharging of the device. A model consisting of a linear resistance Rs and a constant phase element is used to describe the super-capacitor impedance and expressions for the voltage across the device, the power, and stored energy are derived using concepts from fractional calculus. Experimental results are shown and an application of the study to super

In the recent decades, applications of chaotic systems have flourished in various fields. Hence, there is an increasing demand on generalized, modified and novel chaotic systems. In this paper, we combine the general equation of jerk-based chaotic systems with simple scaled discrete chaotic maps. Numerical simulations of the properties of two systems, each with four control parameters, are presented. The parameters show interesting behaviors and dependencies among them. In addition, they exhibit controlling capabilities of the ranges of system responses, hence the size of the attractor diagram

In this paper, we discuss the optimal charging and discharging of supercapacitors to maximize the delivered energy by deploying the fractional and multivariate calculus of variations. We prove mathematically that the constant current is the optimal charging and discharging method under R s -CPE model of supercapacitors. The charging and round-trip efficiencies have been mathematically analyzed for constant current charging and discharging. © 2020 The Electrochemical Society ("ECS"). Published on behalf of ECS by IOP Publishing Limited.