Relationship of singular value stability robustness bounds to spectral radius for discrete systems with application to digital filters

Presents additional results and an application for recently obtained stability robustness bounds on linear time-varying perturbations of an asymptotically stable linear time-invariant discrete-time system. The bounds were developed using Lyapunov theory and singular value decomposition, and provide sufficient conditions for maintaining asymptotic stability for both unstructured and structured perturbations in the state-space discrete system model. A derivation is presented for the relationship between the unstructured perturbation bound and the spectral radius of the system model matrix, showing that the normal form realisation of the system gives the largest unstructured perturbation bound. Both the unstructured and structured perturbation bounds are applied to a recursive digital filter and to coefficient truncation as time-invariant examples to illustrate the use of these relations