Robust controllability of interval fractional order linear time invariant stochastic systems

We deal with the robust controllability problem of the fractional order linear time invariant (FO-LTI) stochastic systems with interval coefficients. We present a necessary and sufficient condition for the controllability problem for the case when there is no interval uncertainty. Based on the concept of linear independency of interval vectors, we formulate the approach to check the robust controllability of interval FO-LTI stochastic systems by employing some simple but very effective sufficient condition for checking the linear independency of interval vectors. Finally, an illustrative example is presented. We show that this interval FO-LTI stochastic system is weakly controllable, while the corresponding deterministic system without noise perturbation is uncontrollable.