Abstract
In this paper, we investigate the strict dissipativity and asymptotic stability of digital filters in the direct form with saturation nonlinearity. First, a novel criterion is presented for the (Q, S, R)-\(\alpha \)-dissipativity of single digital filters in the direct form. By selecting the weighting scalar parameters, this condition reduces to the conditions for \(H_{\infty }\), passivity, and mixed \(H_{\infty }\)/passivity performances. Based on this result, a new sufficient criterion is proposed for the (Q, S, R)-\(\alpha \)-dissipativity of interconnected digital filters in the direct form. A condition for the asymptotic stability of interconnected direct-form digital filters is also presented, and three numerical examples are included to show the effectiveness of the developed theoretical results.
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