To derive analytical feedback solution of time- $L_{1}$ optimal control problem is a challenging task. In this regard, this letter proposes an alternative strategy that involves intermittent application of open loop time- $L_{1}$ optimal solution. When disturbances affect the system, such policy is shown to retain the system states to within a small bounded safe region about the origin. The key idea is to switch the processor in between active and idle mode. During the active mode, the states are measured, open-loop optimal control policy is computed and transmitted along the communication link to the actuator. While during the idle mode, the precomputed control profile is applied and rest of the system resources remain inactive. The open loop solution is obtained by solving a set of optimization problems with an additional bound constraint on the update time instances. The bound constraints are derived using an algorithm to ensure that the safe region (defined in terms of attainable set) is always inside the null controllable region or the reachable set. Since attainable and reachable sets are approximated as convex polytopes, the bound constraints are obtained through linear inequalities. Simulation results show that under the proposed control strategy, system achieves practical stability with reduced usage of system resources.