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The emergence of autonomous vehicles (AVs) is expected to revolutionize road transportation in the near future. Although large-scale numerical simulations and small-scale experiments have shown promising results, a comprehensive theoretical understanding to smooth traffic flow via AVs is lacking. In this article, from a control-theoretic perspective, we establish analytical results on the controllability, stabilizability, and reachability of a mixed traffic system consisting of human-driven vehicles and AVs in a ring road. We show that the mixed traffic system is not completely controllable, but is stabilizable, indicating that AVs can not only suppress unstable traffic waves but also guide the traffic flow to a higher speed. Accordingly, we establish the maximum traffic speed achievable via controlling AVs. Numerical results show that the traffic speed can be increased by over 6% when there are only 5% AVs. We also design …