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 ${H}_{\infty}$ performance, $l_2-l_{\infty}$ performance, passivity, and $(\mathcal{Q},\mathcal{S},\mathcal{R})\mbox{-}\alpha$ -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.
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