FAQ: Are there rigorous ways of determining if it's impossible to meet certain/multiple performance specifications?
Posted by Lars Cremean, 20 November 2002
In short, yes, but there are really no tried-and-true methods that can be applied to general problems and are in the scope of this course.
On the other hand, if your specifications consist of a number of equalities or inequalities over some vector space (e.g. of states, inputs, frequency response or some combination thereof), it's reasonable to pose the problem of determining the region (maybe null) in the vector space that is the intersection of these constraints.