Discrete Time Stability Margins from Stein´s Equation

This paper deals with the robust stability of a discrete time stable state space system subject to structured real parameter uncertainty. Using Lyapunov´s Theorem and Stein´s equation the radius of a stability hypersphere in parameter space is derived from the structure matrices, with the property that all for parameter perturbations lying within the hypersphere stability of the system matrix is preserved. A numerical example is provided.