Backstepping Control of a Class of Continua of Linear Hyperbolic PDEs^∗

We develop a backstepping control design for a class of continuum systems of linear hyperbolic PDEs, described by a coupled system of an ensemble of rightward transporting PDEs and a (finite) system of m leftward transporting PDEs. The key analysis challenge of the design is to establish well-posedness of the resulting ensemble of kernel equations, since they evolve on a prismatic (3-D) domain and inherit the potential discontinuities of the kernels for the case of n + m hyperbolic systems. We resolve this challenge generalizing the well-posedness analysis of Hu, Di Meglio, Vazquez, and Krstic to continua of general, heterodirectional hyperbolic PDE systems, while also constructing a proper Lyapunov functional.