  In this paper, we discuss the relationships between capacity of control in
entropy theory and intrinsic properties in control theory for a class of finite
dimensional stochastic dynamical systems described by a linear stochastic
differential equations driven by mixed fractional Brownian motion with delay in
control. Stochastic dynamical systems can be described as an information
channel between the space of control signals and the state space. We study this
control to state information capacity of this channel in continuous time. We
turned out that, the capacity of control depends on the time of final state in
dynamical systems. By using the analysis and representation of fractional
Gaussian process, the closed form of continuous optimal control law is derived.
The reached optimal control law maximizes the mutual information between
control signals and future state over a finite time horizon. The results
obtained here are motivated by control to state information capacity for linear
systems in both types deterministic and stochastic models that are widely used
to understand information flows in wireless network information theory.
  The contribution of this paper is that we propose some new relationships
between control theory and entropy theoretic properties of stochastic dynamical
systems with delay in control. Finally, we present an example that serve to
illustrate the relationships between capacity of control and intrinsic
properties in control theory.
