This work discuss the robust stabilization problem for discrete-time switched singular systems with simultaneous presence of time-varying delay and sensor nonlinearity. To this end, an observer-based controller was synthesized that works under asynchronous switching signals. Investigating the average dwell time approach and using a Lyapunov-Krasovskii functional with triple sum terms, sufficient conditions were derived for achieving the existence of such asynchronous controller and guaranteeing the resulting closed-loop system to be exponentially admissible with H & INFIN; performance level. Subsequently, the effectiveness of the proposed control scheme was verified through two numerical examples.