Calculation of the structured singular value with gradient based optimization algorithms
Cheng Yi, Jeroen Dehaene, Bart De Moor · 2005
The structured singular value problem, which is a basic problem in robustness analysis and synthesis for control systems with structured uncertainties, can be formulated as an optimization problem over the manifold of unitary matrices with a given structure. The authors show how geometric optimization methods, such as the steepest ascent method and the conjugate gradient method for optimization on a Riemannian manifold, lead to algorithms with guaranteed convergence to a lower bound for the structured singular value.