On closed-loop objectives and guaranteed robustness properties

The usual approach in robust control has been to start with an explicit representation of the plant uncertainty and then look for a way of guaranteeing the satisfaction of some performance objective with the real plant. Here we consider a complementary approach: if a controller satisfies a condition involving a nominal plant, then over what set of plants is it guaranteed to satisfy some closed-loop objective? This viewpoint has several benefits. It can provide less conservative results, and can provide insights into how closed-loop objectives should be chosen for robustness in the absence of hard bounds on the uncertainty