Exponential stability of networks of density-flow conservation laws under PI boundary control

We consider a class of density-flow networks, described by hyperbolic conservation laws, which can be monitored and controlled at the junctions. These control systems are open-loop unstable and subject to unmeasured flow disturbances. We address the problem of feedback stabilization and disturbance rejection under PI boundary control. Explicit stability conditions in the frequency domain are provided. These conditions can also be established in the time domain by using appropriate quadratic Lyapunov functions.