An Enhanced Criterion for Induced $H_{\infty}$ Stability of Discrete-time Systems with Time-varying Delay and External Disturbance

This paper presents an enhanced approach for induced $H_{\infty}$ stability of discrete-time systems in the occurrence of external disturbance and time-varying delay. The presented approach considers a suitable Lyapunov function and its forward difference is estimated using Jensen inequality, yields less conservative result. Delay-partitioning method is introduced for partitioning the delay interval into subintervals. A comparison of the presented criteria with the existing method is shown. The efficacy of the presented criteria is showed with an example.