Real stability radii and quadratic matrix inequality (Q1364950)

A problem from robustness analysis is formulated as a parametric optimization problem. Consider the system \(dx/dt= (A+B\theta C)x\) with real matrices, and a fixed open set \(G\) in the complex plane. The system is said to be stable relative to \(G\) if \(G\) contains all eigenvalues of \(A\). Consider the matrix \(\theta\) as a parameter and denote its largest singular value by \(f^0(\theta)\). The authors consider the problem of minimizing \(f^0(\theta)\) so that the system is not \(G\)-stable. Under the linear constraint \(B=\theta A\), the problem reduces to \[ \inf_{\alpha>0} \{\alpha: \alpha^2 A^T A- B^TB\geq 0\}. \]