# Can $\mu$-analysis apply to robust D-stability analysis?

The $\mu$-analysis is known to give the minimum norm of the uncertain diagonal matrix $\bf{\Delta}$ that cause the $\bf{M}$-$\bf{\Delta}$ system to be unstable.

The above term "unstable" refers to the condition when at least one eigenvalue rests on the right half plane.

However, I am wondering if the concept of "stability" of $\mu$-analysis can be extended to D-stability?

Here D is a defined region in the complex plane, and "stable" is defined as the condition when all eigenvalues rest within D.

• One 'cheap' way would be to find a rational conformal map that maps $D$ to the open left half plane. – copper.hat Feb 3 '18 at 8:06
• It seems related to the circle criterion or popov criterion – Carlos Feb 5 '18 at 7:36