  We study the possibility to stabilize unstable steady states and unstable
periodic orbits in chaotic fractional-order dynamical systems by the
time-delayed feedback method. By performing a linear stability analysis, we
establish the parameter ranges for successful stabilization of unstable
equilibria in the plane parametrizad by the feedback gain and the time delay.
An insight into the control mechanism is gained by analyzing the characteristic
equation of the controlled system, showing that the control scheme fails to
control unstable equilibria having an odd number of positive real eigenvalues.
We demonstrate that the method can also stabilize unstable periodic orbits for
a suitable choice of the feedback gain, providing that the time delay is chosen
to coincide with the period of the target orbit. In addition, it is shown
numerically that delayed feedback control with a sinusoidally modulated time
delay significantly enlarges the stability region of the steady states in
comparison to the classical time-delayed feedback scheme with a constant delay.

General Physics