This paper considers robust performance analysis and state feedback design 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 shown that most robust performance analysis and synthesis problems under this strongly robust H infinity performance criterion can be transformed into linear matrix inequality problems, and can be solved through finite-dimensional convex programming. The results are in general less conservative than those using small gain type criteria.