COMPUTATION OF THE MAXIMAL ROBUST H-2 PERFORMANCE RADIUS FOR UNCERTAIN DISCRETE-TIME-SYSTEMS WITH NONLINEAR PARAMETRIC UNCERTAINTIES

In this paper we address the problems of robust stability and robust H -2 performance for uncertain discrete time systems with nonlinear para metric uncertainties. We consider two families of systems with paramet ric uncertainties described by state-space models which offer a fairly general representation of most uncertain systems with one or two para meters (the approach can be extended to more parameters). For these tw o families we obtain explicit expressions for the Schur stability radi us and for the H-2 robust performance radius in the case of uncertaint ies with a single parameter. Moreover, we provide a line search algori thm for these two problems in the case of two parameters. Both for the robust stability and the robust performance problem, explicit necessa ry and sufficient conditions are derived.