Numerical Analysis of Exponential and BIBS Stability for Linear Discrete Time-Variant Systems using Bohl Exponents

Abstract

This work deals with the stability analysis of linear discrete-time time-variant systems, focusing on the most restrictive stability measures for free respectively forced systems, the exponential stability respectively BIBS (bounded-input bounded-state) stability. Additionally the connection of these stability concepts with the so-called Bohl exponent is in focus of this work. The Bohl exponent can be seen as a generalization of eigenvalues for the stability analysis of time-variant systems. The contribution of this work is the combination of the exponential and BIBS stability analysis with the numerical computation of the Bohl exponent, leading to a numerical stability analysis for linear discrete-time time-variant systems. This stability analysis is applied at a time-variant drivetrain control loop.