The robustly resilient memory control problem is addressed for a class of switched systems with time delay under asynchronous switching. By resorting to the piecewise Lyapunov–Krasovskii functional, an asynchronous memory controller is designed to ensure the exponential stability of the closed-loop system. Here, the piecewise Lyapunov–Krasovskii functional means that for the activated subsystem, the associated Lyapunov–Krasovskii functional on the unmatched interval is different from that on the matched interval. Then an asynchronously resilient memory controller is derived to guarantee that the corresponding closed-loop system is robustly exponentially stable for all the admissible uncertainties. All the conditions are cast into the form of linear matrix inequalities. Finally, a numerical example is provided to illustrate the validity of the proposed results.