Generalized Dissipativity Analysis of Digital Filters with Finite-Wordlength Arithmetic

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∞ performance, l₂ − l∞ performance, passivity, and (Q, S,R)-α-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.Choon Ki Ahn, Peng Sh