Stability robustness of linear discrete-time systems under time-varying perturbations

Abstract

The stability robustness of an asymptotically stable linear time-invariant discrete-time nominal system subject to linear time-varying perturbations is analysed. Based on the stability theory of linear time-varying continuous-time systems and the matrix norm theory, both the norm bounds and the element bounds on linear time-varying perturbations are obtained for the nominal system. The new bounds are simple to implement and they have less conservative results when the condition number of the transformation matrix is small.