Convexity Property of the One-sided Multivariable Stability Margin

In evaluating the stability robustness of multivariable control systems having "one-sided" parameter uncertainty, a problem that naturally arises is the minimization over diagonal matrices D of the greatest eigenvalue of (e^D Ae^-D + (e^D Ae^-D)*)/2. The minimization is proved to be convex, thus guaranteeing that every local minimum, is also a global minimum and, in theory, guaranteeing the global convergence of generalised gradient nonlinear programming algorithms for computing the minimizing D.