Fractional order system

A new fractional-order Lorenz-like system with two stable
node-foci has been thoroughly studied in this paper. Some
sufficient  conditions for the local stability of equilibria
considering both commensurate and incommensurate cases are given.
In addition, with the effective dimension less than three, the
minimum effective dimension of the system is approximated as
2.8485 and is verified numerically. It should be affirmed that the
linear differential equation in fractional-order Lorenz-like
system appears to be less sensitive to the damping, represented by
a fractional derivative, than the two other non-linear equations.
Furthermore, combination synchronization of this system is
analyzed with the help of nonlinear feedback control method.
Theoretical results are verified by performing numerical
simulations.

Citation: Zeeshan Alam, Liguo Yuan, Qigui Yang. Chaos and combination synchronization of a new fractional-order system with two stable
node-foci. IEEE/CAA Journal of Automatica Sinica, 2016, 3(2): 157-164

In approximation of fractional order systems, a significant
objective is to preserve the important properties of the original
system. The monotonicity of time/frequency responses is one of these
properties whose preservation is of great importance in
approximation process. Considering this importance, the issues of
monotonicity preservation of the step response and monotonicity
preservation of the magnitude-frequency response are independently
investigated in this paper. In these investigations, some conditions
on approximating filters of fractional operators are found to
guarantee the preservation of step/magnitude-frequency response
monotonicity in approximation process. These conditions are also
simplified in some special cases. In addition, numerical simulation
results are presented to show the usefulness of the obtained
conditions.

Citation: Mohammad Saleh Tavazoei. Criteria for response monotonicity preserving in approximation of fractional
order systems. IEEE/CAA Journal of Automatica Sinica, 2016,
3(4): 422-429

Studies on analysis, design and applications of analog and digital differentiators and integrators of fractional order is the main objective of this paper. Time and frequency domain analysis, different ways of realization of fractance device is presented. Active and passive realization of fractance device of order 12 using continued fraction expansion is carried out. Later, time and frequency domain analysis