L₂-l_∞ stability criterion for fixed-point state-space digital filters with saturation nonlinearity

This article proves that there exists an l₂-l_∞ stability criterion for fixed-point state-space digital filters without overflow oscillations. By the l₂-l_∞ stability property, this new criterion guarantees asymptotic stability and attenuates the effect of external interference to a prescribed l₂-l_∞-induced norm bound. We represent this stability criterion as the form of linear matrix inequality, which can be solved easily using the existing numerical packages. Finally, we present an illustrative example, which shows the effectiveness of the proposed stability criterion.