This paper proposes a new criterion for the input/output-to-state stability (IOSS) of direct-form digital interference filters with finite values. word length nonlinearity based on an augmented Lyapunov function. Without external interference, the output-state stability (OSS) and asymptotic stability of direct form digital filters with finite word length nonlinearity are also guaranteed according to the proposed criterion. This criterion is expressed by linear matrix inequalities (IMT). A numerical example demonstrates the effectiveness of the proposed criterion. Keywords: input/output stability to state (IOSS); on-state output stability (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 are unstable behavior and should be avoided in digital filter design[?]. Thus, determining the range of digital filter coefficients, where these limit cycles must be avoided, is very important. Much attention has been paid to 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 decompose it into several lower-order digital filters before implementation. In this case, mutual interference inevitably occurs between these lower order filters, resulting in malfunctions as well as poor performance...... middle of paper ......which guarantees IOSS when and the OSS and asymptotic stability in this example. To leave . 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 to the origin when .Figure 1: Phase plot whenFigure 2: Phase plot when5 ConclusionIn this paper, we proposed a new LMI-based criterion for the IOSS of digital filters direct form interference with saturation overflow nonlinearity. . Based on the augmented Lyapunov function, the criterion also guarantees the OSS and asymptotic stability of direct form digital filters without external interference under the additional LMI condition. The criterion is expressed by the LMIs. An example has been provided to demonstrate the proposed criterion.