How to formulate linear control problem for Stochastic Differential Equation solvers

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I have the following linear control problem:
x'(t) = A*x(t) + B*u(t)
y(t) = C*x(t) + D*u(t)
where
x(t0) = x0 ... initial condition
and
y(t) .... is system output signal
A,B,C and D .... are real square matrices with constant coefficients (in my case are matrices small ... 2 x 2)
u(t) ... is discrete (measured!!!) vector signal contaminated by noise and errors
My questions are:
  • How to properly formulate this problem as Stochastic Differential Equation (SDE) task? Because of signal u(t) stochastic behavior the standard ODE solvers are not adequate tools.
  • How to estimate proper noise (error) model of signal u(t)?
  • what TMW toolboxes or FEX packages are available to solve this problem?

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