Input-to-state stability of coupled hyperbolic PDE-ODE systems via boundary feedback control

We herein investigate the boundary input-to-state stability(ISS) of a class of coupled hyperbolic partial differential equation-ordinary differential equation(PDE-ODE) systems with respect to the presence of uncertainties and external disturbances. The boundary feedback control of the proportional type acts on the ODE part and indirectly affects the hyperbolic PDE dynamics via the boundary input. Using the strict Lyapunov function, some sufficient conditions in terms of matrix inequalities are obtained for the boundary ISS of the closed-loop hyperbolic PDE-ODE systems. The feedback control laws are designed by combining the line search algorithm and polytopic embedding techniques. The effectiveness of the designed boundary control is assessed by applying it to the system of interconnected continuous stirred tank reactor and a plug flow reactor through a numerical simulation.