Robust Schur stability and robust ℋ2 performance for uncertain systems with nonlinear parametric uncertainties

The problems of robust stability and robust ℋ₂ performance for uncertain discrete time systems with nonlinear parametric uncertainties are addressed. Two fairly general families of state space models depending nonlinearly on one or two uncertain parameters are considered. For these two families explicit expressions for the Schur stability radius and for the ℋ₂ robust performance radius in the case of uncertainties with a single parameter are obtained, and a line search algorithm for the two problems in case of two parameters is provided. For both problems explicit necessary and sufficient conditions are derived. An illustrative example demonstrates the algorithms