Characterization and efficient computation of the structured singular value

The concept of structured singular value was recently introduced by Doyle [1] as a tool for the analysis and synthesis of feedback systems with structured uncertainties. It is a key to the design of control systems under joint robustness and performance specifications and it very nicely complements the
H^{\infty}
approach to control system design. in this paper, it is shown that the structured singular value can be obtained as the solution of several smooth optimization problems. Properties of these optimization problems are exhibited, leading to a fast algorithm that always yields the structured singular value for block structures of size no larger than 3, and often does for block structures of larger size.