Robust stability and performance of uncertain systems in state space

Robust performance analysis and state feedback design are considered for systems with time-varying parameter uncertainties. The notion of a strongly robust H_∞ 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 scaled small gain criterion. It is shown that most robust performance analysis and synthesis problems under this strongly robust H_∞ 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 obtained using small-gain-type criteria