Evaluation and comparison of integer-order approximations for fractional integrators for application to fractional-order Chua systems

This paper deals with the study of effect of fractional operators in chaotic systems. Chaos means randomness and irregularity. Some of the typical features of chaos are non-linearity, determinism, sensitivity to initial conditions and irregularity. In this paper, three s-to-z transformations viz. Tustin, Al-Alaoui and Maneesha-Pragya-Visweswaran operators have been used to obtain integer order approximations of fractional integrators in z-domain. The stability of the proposed models has been investigated. These discretizations can be applied for analysis of fractional order Chua systems. A comparison with the existing approximations is also presented. The major purpose of the paper is to emphasize that the z-domain approximations proposed in this paper can be used for hardware realizations.