Autonomous vehicles (AVs) enable more efficient and sustainable transportation systems. Ample studies have shown that controlling a small fraction of AVs can smooth traffic flow and mitigate traffic congestion. However, deploying AVs to real-world systems is challenging due to transparency and safety concerns. An alternative approach deployable in the imminent future is human-compatible driving, where human drivers are guided by real-time instructions to stabilize the traffic. To respect human drivers’ reaction time $\Delta$, a class of piecewise-constant policies is considered, where periodic instructions are given at every $\Delta$ seconds to human drivers, who hold the instructed action constant until the next instruction. While previous work provides a basic theoretical analysis by considering a single driver setting in the absence of traffic, a principled control theoretic analysis that takes into account the full traffic system is lacking. This work uses Lyapunov stability theory to analyze piecewise-constant policies in a traffic system governed by the Optimal Velocity Model (OVM). We provide sufficient conditions for piecewise-constant controls with hold length $\Delta$ to stabilize the system. Numerical simulations demonstrate that our theoretical analyses closely follow simulated results, and can be used to interpret meaningful relationships between system parameters and maximum stable hold lengths.