Computation of μ with real and complex uncertainties

The robustness analysis of system performance is one of the key issues in control theory, and one approach is to reduce this problem to that of computing the structured singular value, μ. When real parametric uncertainty is included, then μ must be computed with respect to a block structure containing both real and complex uncertainties. It is shown that μ is equivalent to a real eigenvalue maximization problem, and a power algorithm is developed to solve this problem. The algorithm has the property that μ is (almost) always an equilibrium point of the algorithm, and that whenever the algorithm converges a lower bound for μ results. This scheme has been found to have fairly good convergence properties. Each iteration of the scheme is very cheap, requiring only such operations as matrix-vector multiplications and vector inner products, and the method is sufficiently general to handle arbitrary numbers of repeated real scalars, repeated complex scalars, and full complex blocks