Hello,

Could you be a little more specific? Are you doing "actual" LQG (ie combined LQ regulator and LQ estimation, see eg the matlab link attached)? By "increasing the noise covariance" do you mean increasing the matrix QWV with respect to the covariance matrix QXU (I use the notations in the attached link)?

http://fr.mathworks.com/help/control/ref/lqg.html

Dear Philippe,

I am using lqg command directly, and yes I want to see the effect of QWV...

Dear Vishisht,

This is quite a complicated matter, and one of the main problems in linear control theory! It is not really possible to answer your questions in a few lines.

LQG consists of two independent optimization problems: an optimal regulator (determined by the matrix QXU), and an optimal estimator (Kalman filter, determined by the matrix QWU). You can see what the Matlab command lqg actually does that by typing "type lqg". Changing the QWV matrix (without changing the QXU) will influence the robustness of the control law, but not the dynamic performance of the regulator alone. Similarly, changing the QXU matrix (without changing the QWV) will influence the robustness of the control law, but not the dynamic performance of the estimator alone.

You can find a simple historical perspective of the question and some bibliography at the attached link. 

http://www.math.univ-toulouse.fr/~noll/lqg_ltr.html