Stability Radii for Difference Equations with Time-varying Coefficients

Abstract

This paper deals with a formula of stability radii for an linear difference equation (LDEs for short) with the coefficients varying in time under structured parameter perturbations. It is shown that the $l_p-$ real and complex stability radii of these systems coincide and they are given by a formula of input-output operator. The result is considered as an discrete version of a previous result for time-varying ordinary differential equations \cite{Jacob98}.