Some Properties of an Upper Bound for µ

A convex upper bound of the mixed structured singular value ¯ is analyzed. The upper bound is based on a multiplier method. It is simple, it can exploit low-rank properties and it is shown to be less conservative than the well-known (D; G)-scaling. A direct relationship with (D; G)- scaling is given. The upper bound can be modified to one that is continuous with an explicit Lipschitz constant. Keywords--- Mixed structured singular values, linear matrix inequalities, multipliers. I. Introduction One of the nagging problems of robust control is to determine whether or not a system remains stable and retains satisfactory performance qualities under variations and uncertainties of some sort. In an attempt to get a handle on the problem, Doyle [8] introduced in 1982 the structured singular value. The definition of the structured singular value, or ¯ for short, is such that robust stability=robust performance of the control problem is equivalent to ¯ being less than 1. Originally ¯ was de..