This paper considers robust performance analysis and state feedback de
sign for systems with time-varying parameter uncertainties. The notion
of a strongly robust H infinity performance criterion is introduced,
and its applications in robust performance analysis and synthesis for
nominally linear systems with time-varying uncertainties are discussed
and compared with the constant scared small gain criterion. It is sho
wn that most robust performance analysis and synthesis problems under
this strongly robust H infinity performance criterion can be transform
ed into linear matrix inequality problems, and can be solved through f
inite-dimensional convex programming. The results are in general less
conservative than those using small gain type criteria.