The concept of structured singular value was recently introduced by J. C. Doyle as a tool for the analysis and synthesis of feedback systems with structured uncertainties (see Proc. IEE, vol. 6, no. 129, pp. 242-250, 1982). It is a key to the design of control systems under joint robustness and performance specifications and it complements the H infinity approach to control system design. 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 three and often does for block structures of larger size.
