Computation of the complex structured singular value using fixed-structure dynamic D-scales

The complex structured singular value was developed to nonconservatively analyze systems with multiple-block structured uncertainty with arbitrary phase. In practice, optimization techniques are used to compute an upper bound on the structured singular value which has been seen through numerous numerical examples to introduce little conservatism. The standard approach to computing this upper bound involves finding diagonal scaling matrices D(jω) that minimize σ_max(D(jω)G(jω)D^-1(jω)) over a (theoretically) infinite number of frequencies. The order of the corresponding rational function D(s) (if it exists) is hence arbitrary. This paper develops a fixed-structured approach to computing an upper bound for the complex structured singular value. In particular, by relying on results on mixed-norm H₂/H_∞ analysis, D(s) is a priori constrained to be a rational function matrix of a chosen fixed order and a new approach to computing an upper bound on the structured singular value is developed. This new approach lays the foundation for structured singular value controller synthesis that avoids the standard D-K iteration and curve fitting procedure