Discrete Output Regulator Design for a 2D System of first-order Hyperbolic PDEs

This work is concerned with the discrete-time output regulation design for a system of first-order hyperbolic partial differential equations in two spatial dimensions, motivated by applications in continuity equations governing mass balance in fluid systems. Without any model reduction or approximation, an exact closed-form semigroup operator is derived using the Laplace transform in both time and space. This enables the formulation of exact discrete-time system operators. A discrete-time output regulator is designed to ensure setpoint tracking. Additionally, boundary actuation and measurement are utilized for control implementation. The proposed methodology is validated through numerical simulations, demonstrating its effectiveness in regulating the system.