I wonder what $\mu$ – synthesis analysis is? I have heard that is an uncertainty modelling.
I think it's an extra help for the $H_{\infty}$ controller because the $\mu$ – synthesis analysis make sure that the $H_{\infty}$ controller can stand against nonlinearities.
So $\mu$ + $H_{\infty}$ = Robust nonlinear control.
Am I right?
The reason why I'm asking this simple question is that the books which teach robust control, cannot explain why we are going to use $\mu$ – synthesis analysis. They only teach math, not the purpose.
Best Answer
$H_{\infty}$ deals with the problem of finding a controller $F(s)$ for a known system $G(s)$ such that the gain (in $H_{\infty}$ sense) from an external signal to an output is minimized.
$\mu$-synthesis extends this to the case when $G(s)$ is uncertain, and tries to minimize the worst-case gain given the uncertainty description.