Controllability of Time-Varying Stochastic Fractional Dynamical Systems with Distributed Delays in Control

Abstract

Distributed delays present significant challenges for controllability due to their continuous nature and non-local effects. This paper addresses these challenges analytically and presents results on the controllability of linear and nonlinear time-varying stochastic fractional dynamical systems (TV-SFDSs) with distributed delays in control. Using the Bourdin state transition matrix (STM), the solution of the system under consideration is obtained. The controllability criterion is established using a Gramian matrix-based approach. The Banach fixed-point theorem is used to develop the controllability criterion for the nonlinear system. Numerical examples are given to illustrate the application of these results.

Keywords

Fractional dynamical systems / Controllability / State transition matrix (STM) / Gramian matrix technique / 34A08 / 93B07 / 47H10 / 93B05

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Shanghai University