Strictly passive suppression of limit cycles in direct form digital filters with saturation nonlinearity: Linear matrix inequality approach

In this paper, we propose a new linear matrix inequality criterion for suppression of limit cycles in state-space direct form digital filters with saturation arithmetic and external interference via a passivity approach. The passive approach is employed to reduce the effect of external interference on the digital filter. The criterion guarantees not only asymptotic stability but also passivity from the external interference to the output vector. This criterion is in the form of linear matrix inequality; hence, it is computationally tractable. An example shows the effectiveness of the proposed criterion.