This paper proposes a new criterion for the input/output-state stability (IOSS) of interfering direct-form digital filters with finite word length nonlinearities based on an augmented Lyapunov function. Without external interference, the output-state stability (OSS) and asymptotic stability of digital filters in direct form with finite word length nonlinearity are also guaranteed according to the proposed criterion. This criterion is expressed by linear matrix inequalities (LMI). A numerical example demonstrates the effectiveness of the proposed criterion.Keywords: input/output-state stability (IOSS); stability of the output-state relationship (OSS); asymptotic stability; digital filter; finite word length effect1 IntroductionWhen we design and implement digital filters, we use fixed-point arithmetic, which generates overflow and quantization nonlinearities. These nonlinearities can cause digital filters to potentially produce zero-input limit cycles if the digital filter coefficients are not selected appropriately [?]. Zero-input limit cycles represent unstable behavior and should be avoided in digital filter design [?]. Therefore, determining the range of digital filter coefficients, where these limit cycles should be avoided, is very important. Much attention has been focused on the criteria for removing limit cycles in digital filters, including overflow nonlinearity [?, ?, ?, ?, ?, ?, ?, ?, ?, ?]. When we implement a large-scale high-order digital filter using digital hardware and computers, we usually split it into several lower-order digital filters before implementation. In this case mutual interference inevitably occurs between these low-order filters, and this leads to malfunctions as well as poor performance...... middle of the paper ......which guarantee the IOSS when and the OSS and asymptotic stability in this example. Allow . Figure 1 shows that the state variables are bounded around the origin by the IOSS property when, where is a white Gaussian random sequence with mean and variance. Figure 2 shows that the state variables converge towards the origin when .Figure 1: Phase diagram whenFigure 2: Phase diagram when5 Conclusion In this paper, we proposed a new LMI-based criterion for the IOSS of digital filters in direct interfering form with saturation overflow nonlinearity. Based on the augmented Lyapunov function, the criterion also guarantees the OSS and asymptotic stability of digital filters in direct form without external interference in the additional LMI condition. The criterion is expressed by the LMI. An example has been provided to demonstrate the proposed criterion.