I am  not an expert in SDRE, but if you end up with a linearization given by A & B which is not controllable, then it is not controllable, and  you cannot do much to change this fact, unless you are able to change the structure of the physical system somehow (i.e. the differential equations you use to model the system).

However, I do not udnerstand your linearization. Why do you have zeros almost everywhere? For example, the first state equation Xdot = V.cos(theta) does not depend only on V but also on theta, so you should have two nonzero elements in the first row of A. Something like

[0 0 -V*sin(theta) cos(theta) 0]

Similarly for 2nd and 3rd row of your matrix A.

thank you miroslav . but it is the nature SDC form . 

if you product first row of A in state variables which are [x y theta V phi] then it yields 

Xdot = V.cos(theta)

Hello, Salman. Here comes the humble words of another non-expert in the subject SDRE. I hope they can help you a little bit at least. My expertise in control systems allow me to tell you that: i) first of all, an uncontrollable system can never be controlled, and that is so by the definition. The best you can hope for is that the uncontrollable portion of your system is stable. If this isn't the case, then you definitively need to change your system so as to make it controllable; ii) are you sure you're applying the appropriate controllability test? Both the nonlinear systems and the time-varying systems (that seems to be the case, when it comes to the linearised state-dependent matrices you mentioned) require a slightly more complex controllability test to be performed. I'd recommend you to check that out first. Very good luck with your work! :-)

thank you Daniel .this is obvious that an uncontrollable System cannot be controlled. but in the context of SDRE approach , we build a linearized form of nonlinear system while this linearized shape is not unique and by algebric manipulation every body can propose different kind of linearized form. for a multivaribale non-linear system it can be proved that there are infinite number of state dependent matrix coefficient .

fortunately right now i could reach another form for this system which is much more better in sense of controllabilitiy . anyway thank you.

live long and prosper .

Hi Salman

Maybe it is late.

For SDRE control there are existence conditions that should be met, one of them is controlability of the chosen parametric linearization. If there is no such parametrization or cannot be found then SDRE cannot work.

Please read the following paper for more information:

" State-Dependent Riccati Equation (SDRE) Control: A Survey "

I hope this answers your question.