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In this paper, we discuss the relationships between capacity of control inentropy theory and intrinsic properties in control theory for a class of finitedimensional stochastic dynamical systems described by a linear stochasticdifferential equations driven by mixed fractional Brownian motion with delay incontrol. Stochastic dynamical systems can be described as an informationchannel between the space of control signals and the state space. We study thiscontrol to state information capacity of this channel in continuous time. Weturned out that, the capacity of control depends on the time of final state indynamical systems. By using the analysis and representation of fractionalGaussian process, the closed form of continuous optimal control law is derived.The reached optimal control law maximizes the mutual information betweencontrol signals and future state over a finite time horizon. The resultsobtained here are motivated by control to state information capacity for linearsystems in both types deterministic and stochastic models that are widely usedto understand information flows in wireless network information theory.  The contribution of this paper is that we propose some new relationshipsbetween control theory and entropy theoretic properties of stochastic dynamicalsystems with delay in control. Finally, we present an example that serve toillustrate the relationships between capacity of control and intrinsicproperties in control theory.

Capacity of Control for Stochastic Dynamical Systems Perturbed by Mixed Fractional Brownian Motion with Delay in Control