ℋ∞ optimization with spatial constraints

A generalized ℋ∞ synthesis problem where non-euclidian spatial norms on the disturbances and output error are used is posed and solved. The solution takes the form of a linear matrix inequality. Some problems which fall into this class are presented. In particular, solutions are presented to two problems: a variant of ℋ∞ synthesis where norm constraints on each component of the disturbance can be imposed, and synthesis for a certain class of robust performance problems.