Purpose

This paper deals with the problem of input/output-to-state stability (IOSS) of direct-form digital filters, which simultaneously contain external disturbances and two's complement nonlinearity. The nonlinearity under consideration is confined to the sector [–1, 1], which contains saturation, zeroing, two's complement and triangular.

Design/methodology/approach

The proposed condition is based on IOSS approach, which is capable of providing a framework for checking and analysing the stability of nonlinear system based on input as well as output information.

Findings

A linear matrix inequality (LMI)-based new sufficient criterion for the IOSS of the suggested system is obtained. The obtained criterion is capable of detecting the output-to-state stability (OSS) and asymptotic stability of direct-form digital filters with zero external disturbances. In addition, state-norm estimator for the filter under consideration is constructed by adopting an exponential-decay IOSS criterion. Several examples are provided to illustrate the usefulness of the proposed criteria.

Originality/value

The result of the paper is introduced for the first time, and it is suitable for stability analysis of interfered direct-form digital filter with two's complement overflow using IOSS approach.

中文翻译：

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实现具有单二进制补码非线性的受干扰直接型数字滤波器的新结果

目的

本文涉及同时包含外部干扰和二进制补码非线性的直接型数字滤波器的输入/输出状态稳定性 (IOSS) 问题。所考虑的非线性仅限于扇区 [–1, 1]，其中包含饱和、归零、二进制补码和三角形。

设计/方法/方法

所提出的条件基于IOSS方法，该方法能够为基于输入和输出信息检查和分析非线性系统的稳定性提供框架。

发现

获得了基于线性矩阵不等式 (LMI) 的建议系统 IOSS 的新充分准则。所获得的准则能够检测具有零外部干扰的直接形式数字滤波器的输出状态稳定性（OSS）和渐近稳定性。此外，所考虑的滤波器的状态范数估计器是通过采用指数衰减 IOSS 准则构建的。提供了几个例子来说明拟议标准的有用性。

原创性/价值

论文结果为首次介绍，适用于采用IOSS方法进行二进制补码溢出的受干扰直接型数字滤波器的稳定性分析。