Worst-case performance analysis with constrained uncertainty

In this paper, we examine the worst-case performance of a linear system with real parametric uncertainty. In particular, we will analyze the worst-case gain from disturbances to errors of a system subjected to 2 real, scalar uncertainties. The 2 scalar uncertainties are typically normalized so that they have absolute value less than or equal to one. In the parameter space, this constrains the uncertainties to lie in the unit cube. The contribution of this paper is that we also assume that the 2 scalar parameters are correlated. This correlation is represented by an additional offset rectangle constraint in the parameter space. The motivation for this problem is to use our knowledge of parameter correlation to remove some of the conservativeness in the standard performance analysis.