Stability of Discrete-Time Delayed Systems Subject to External Interference and Generalized Overflow Nonlinearities

This article concerns the stability of delayed discrete-time systems (DTSs) through
${H_\infty }$
performance under external interference and generalized overflow nonlinearities. The novel criteria that analyze the exponential stability of DTSs with constant state delays are presented. Moreover, an extension to attain the
${H_\infty }$
performance is developed to handle the external interference of systems with time-varying delays based on Wirtinger-based inequality and reciprocal convex inequality. For such systems, the presented approach ensures zero-input overflow stability as well as robustness against interferences with a guaranteed
${H_\infty }$
level. The presented methodology can also be applied to determine the minimum attenuation level to achieve the desirable performance specifications for the sake of hardware optimization. The presented criteria are less conservative than several existing criteria. The efficacy of the presented criteria is exemplified by examples.