I need to generate a small probing noise in Matlab to implement a least square estimation algorithm. The noise $v(t)$ should be added to input $u(t)=-Kx(t)+v(t)$ of the linear dynamical system $\dot{x}(t)=Ax(t)+Bu(t)$, $y(t)=cx(t)$, $x\in\mathcal{R}^6$.
I also need $v(t)$ to be positive. I am not sure whether I can use v(t)=abs(rand())or v(t)=abs(awgn())? How can I check whether such an input meets persistent excitation condition required for estimation? I would also like to limit the magnitude of $v(t)$ to be very less compared to $-Kx(t)$ but $u(t)$ should sufficiently excite my system to facilitate parameter identification. Also usual noise generation commands has options in terms signal processing aspect such as signal-to-noise ratio, decibel etc, I wonder how can I relate it to excitation of all modes of a linear dynamical system? What SNR and dB is sufficient to meet persistent excitation condition?
Any clue? even some general tips guidelines or references will help.
Is adding small magnitude white noise generally sufficient ? I ask this as I read that "A stationary signal is PE of order $n$ if its frequency spectrum is non zero for at least n points. White noise is PE of any order." So in general adding white noise suffices?
Thank you...