New Criterion for l2-l∞ Stability of Interfered Fixed-Point State-Space Digital Filters with Quantization/Overflow Nonlinearities

The problem of l(2)-l stability and disturbance attenuation performance analysis of fixed-point state-space digital filters with external disturbance and finite wordlength nonlinearities is studied in this paper. The finite wordlength nonlinearities are composite nonlinearities representing concatenations of quantization and overflow correction employed in practice. Using sector-based characterization of the finite wordlength nonlinearities, a new l(2)-l stability criterion for the reduction of the effects of external disturbance to a given level and to confirm the nonexistence of limit cycles in the absence of external interference is established. Numerical examples are given to illustrate the efficacy of the proposed criterion.