We propose a new concept named sub-schedulability to relax schedulability conditions on task sets in the context of scheduling and control co-design. Sub-schedulability is less conservative compared to schedulablity requirement with respect to network utilization. But it can still guarantee that all tasks can be executed before or within a bounded time interval after their deadlines. Based on the sub-schedulability concept, we derive an analytical timing model to check the sub-schedulability and perform online prediction of time-delays caused by real-time scheduling. A modified event-triggered contention-resolving MPC is presented to co-design the scheduling and control for the sub-schedulable control tasks. Simulation results are demonstrated to show the effectiveness of the proposed method.