State feedback output regulation for a class of hyperbolic PDE systems

This work focuses on the development of a state feedback regulator for a class of first order hyperbolic PDE systems with spatially varying coefficients and single point observation. The plant is assumed to be exponentially stabilizable and driven by a linear finite dimensional exosystem which is neutral stable and generates the reference signal and disturbance for the plant. The regulator design problem is to control the fixed plant such that the plant output tracks the reference signal and/or rejects the disturbance. Under the standard assumption of stabilizability, this work shows that the solvability of a constrained Sylvester equation is sufficient to guarantee the solvability of the regulator problem. Moreover, the Riccati and Lyapunov equations are utilized to provide a choice of stabilizing feedback gain which guarantees the closed-loop stability. An adequate numerical example of constant tracking for the first order hyperbolic PDE system with spatially varying coefficients is explored within the proposed regulator design.