How can I obtain the objective function from the state space equations?

I have a state space model;

dx/dt=Ax+Bu; Y=Cx+Du;

And objective function;

F=x'*H*x+c'*x

and some inequality constraints

Can somebody please tell me whether there is a direct relationship between Hessian matrix (H) and the state space matrices (A, B, C, D)? If yes, is there any matlab function to obtain the hessian from state space matrices?

[Shashank Prasanna]

Where did you get the second equation from?