Multivariable PI controller design for 2 × 2 systems governed by hyperbolic partial differential equations with Lyapunov techniques

This paper addresses the multivariable PI regulation control of a class of linear systems described by hyperbolic partial differential equations. Both the input control and the output measurement are situated on the boundary. First, the system is transformed into the characteristic form of Riemann invariants, and the PI controller design is proposed for the Riemann invariant system. Then, a Lyapunov functional is constructed to prove stabilization and regulation of the closed-loop system. Finally, we apply the designed PI controller for a nonlinear Saint-Venant model and carry out numerical simulations to evaluate the performances of the designed PI controller.