Some new results on the stability of direct-form digital filters with finite wordlength nonlinearities

This paper proposes a new criterion for the input/output-to-state stability (IOSS) of interfered direct-form digital filters with finite wordlength nonlinearities based on an augmented Lyapunov function. Without external interferences, the output-to-state stability (OSS) and asymptotic stability of direct-form digital filters are guaranteed under the proposed criterion. An improved criterion is also proposed for the IOSS and OSS of interfered direct-form digital filters, with the introduction of four slack matrices. A new state-norm estimator for direct-form digital filters is constructed based on an exponential-decay IOSS criterion. The criteria presented in this paper are expressed by linear matrix inequalities (LMIs). Two numerical examples demonstrate the effectiveness of the proposed results.