On Stability of Discrete-Time LTI Systems With Varying Time Delays

Abstract

This technical note concerns robust stability analysis of discrete-time linear-time-invariant (LTI) systems with varying time delays. The stability problem is tackled under the integral quadratic constraint (IQC) framework. The time-delay system in question is viewed as feedback interconnection of an LTI stable operator and the so-called “delay-difference” operator, for which IQC characterizations are required in order to apply IQC analysis. One of the main contributions of the technical note is to derive novel IQC characterizations for the “delay-difference” operator, based on the assumption that the time-varying delay parameter and its variation are bounded. A set of new stability criteria emerges as the result. Numerical examples are given to illustrate the effectiveness of the new stability criteria. Another distinct contribution is the idea of introducing bounds on the so-called “ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -step total variation” and “ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -step average variation” of the time-varying delay parameter, which is proven to be useful in stability analysis.