  Control of mixed-autonomy traffic where Human-driven Vehicles (HVs) and
Autonomous Vehicles (AVs) coexist on the road has gained increasing attention
over the recent decades. This paper addresses the boundary stabilization
problem for mixed traffic on freeways. The traffic dynamics are described by
uncertain coupled hyperbolic partial differential equations (PDEs) with Markov
jumping parameters, which aim to address the distinctive driving strategies
between AVs and HVs. Considering that the spacing policies of AVs vary in mixed
traffic, the stochastic impact area of AVs is governed by a continuous Markov
chain. The interactions between HVs and AVs such as overtaking or lane changing
are mainly induced by impact areas. Using backstepping design, we develop a
full-state feedback boundary control law to stabilize the deterministic system
(nominal system). Applying Lyapunov analysis, we demonstrate that the nominal
backstepping control law is able to stabilize the traffic system with Markov
jumping parameters, provided the nominal parameters are sufficiently close to
the stochastic ones on average. The mean-square exponential stability
conditions are derived, and the results are validated by numerical simulations.
