Controllability of Stochastic Delay Systems Driven by the Rosenblatt Process

In this work, we consider dynamical systems of linear and nonlinear stochastic delay-differential equations driven by the Rosenblatt process. With aid delayed matrix functions these systems, derive controllability results as an application. By using a delay Gramian matrix, provide sufficient necessary criteria for systems. addition, employing Krasnoselskii’s fixed point theorem, present some Our improve extend existing ones. Finally, example is given to illustrate main results.