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.
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.
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.
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.
