Relative controllability of a stochastic system using fractional delayed sine and cosine matrices - Wang, JinRong; Sathiyaraj, T.; O’Regan, Donal (Nonlinear Analysis: Modelling and Control, 2021)
In this paper, we study the relative controllability of a fractional stochastic system with pure delay in finite  dimensional stochastic spaces. A set of sufficient conditions is obtained for relative exact controllability using fixed point theory, fractional calculus (including fractional delayed linear operators and Grammian matrices) and local assumptions on nonlinear terms. Finally, an example is given to illustrate our theory.
Keywords: relative controllability; fractional delay stochastic systems; fractional delayed sine and cosine matrices