Improved Criterion for Robust Stability of Discrete-Time State-Delayed Systems with Quantization/Overflow Nonlinearities

This paper deals with the problem of global asymptotic stability of discrete-time state-delayed digital filters under norm-bounded parameter uncertainties and the composite effects of quantization and overflow nonlinearities. A novel approach to identify the composite nonlinearities, in the underlying uncertain system, which effectively operates only in quantization region, is adopted. Utilizing the maximum normalized quantization error of quantizer, the maximum representable number for a given wordlength and an estimated upper bound of parameter uncertainties, along with system parameters, a new global asymptotic stability criterion is established. The criterion is compared with the existing criterion. The usefulness of the presented result is demonstrated with the help of an example.