Numerical algorithms for the largest structured singular value of a \(\mu\)-synthesis control system (Q987882)

For a given stable feedback system with \(M(s) = C(sI-A)^{-1}B\) as its transfer function and an uncertain perturbation \(\Delta(s)\), the authors develop a bisection algorithm and a Newton like algorithm to estimate the margin \(\| \Delta\|_\infty\) for which the system perturbed by \(\Delta(s)\) remains stable, specifically for diagonal uncertainties \(\Delta\). This is an optimization problem with linear matrix constraints. Numerical examples show the advantage of the locally quadratically convergent Newton like method, especially if preceded by a few iterations of the bisection algorithm to move into the region of attracting starting points for the Newton method.