On Exact Robust Instability Radius of Discrete-time LTI Systems

Abstract

Robust instability analysis is intimately related to minimum-norm strong stabilization and arises in the study of oscillatory behavior in nonlinear systems. This paper analyzes the robust instability of linear discrete-time systems against stable perturbations in a direct manner without the use of bilinear transformations, and notes several important differences from its continuous-time counterpart. The results in this paper are particularly useful in the context of sampled-data control, in which the plant is often discretized for control synthesis purposes and minimum-norm strong stabilization in discrete-time is of interest.