What is $\mu$ - synthesis analysis? Uncertainty modelling 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.

$H_\infty$ deals with minimizing the influence of uncertainty in your plant, but the uncertainty is unstructured, i.e. each uncertainty in your plant couples with every other. Generally this is not the case in most problems. For a harmonic oscillator, the uncertainty in the mass should not couple with the uncertainty in the spring constant. H-inf assumes this is the case.

$\mu$-synthesis attempts to deal with structured uncertainty.

Therefore, $H_\infty$ produces more conservative controllers that might not be able to meet the design specs. Using u-synthesis you can increase the performance of the system while still meeting the requirement that the induced disturbances from the uncertainty remain below a certain level.