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Modern Cyber-Physical Systems (CPSs) are often designed as networked, software-based controller implementations which have been found to be vulnerable to network-level and physical level attacks. A number of research works have proposed CPS-specific attack detection schemes as well as techniques for attack resilient controller design. However, such schemes also incur platform-level overheads. In this regard, some recent works have leveraged the use of skips in control execution to enhance the resilience of a CPS against false data injection (FDI) attacks. In this paper, we provide an analytical discussion on when and how skipping a control execution can improve the resilience of the system against FDI attacks while maintaining the control performance requirement. We also propose a methodology to synthesize such optimal control execution patterns. To the best of our knowledge, no previous work has provided any quantitative analysis about the trade-off between attack resilience and control performance for such aperiodic control execution. Finally, we evaluate the proposed method on several safety-critical CPS benchmarks.