Generalized Dissipativity Analysis of Digital Filters With Finite-Wordlength Arithmetic

Abstract

This brief investigates the generalized dissipativity of digital filters with finite-wordlength arithmetic. First, a new sufficient condition is proposed to guarantee the generalized dissipativity of single digital filters with finite-wordlength arithmetic. Unlike the existing works in the literature, this brief presents criteria for H-infinity performance, l(2)-l(infinity) performance, passivity, and (Q, S, R)-alpha-dissipativity in a unified framework. Based on this result, we examine the generalized dissipativity of feedback interconnected digital filters as well as the asymptotic stability of unforced feedback interconnected digital filters. A numerical example demonstrates the effectiveness of the obtained approach.