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

Automated summary

In this work, we study dynamical systems of linear and nonlinear stochastic delay-differential equations driven by the Rosenblatt process. We derive the controllability results for these systems using delayed matrix functions. By using a delay Gramian matrix and Krasnoselskii's fixed point theorem, we provide sufficient and necessary criteria for the controllability of linear and nonlinear stochastic delay systems. Our results improve and extend existing ones and an example is given to illustrate the main findings.