Control of a 2 × 2 coupled linear hyperbolic system sandwiched between 2 ODEs

Abstract

SummaryMotivated by an engineering application in cable mining elevators, we address a new problem on stabilization of 2×2 coupled linear first‐order hyperbolic PDEs sandwiched between 2 ODEs. A novel methology combining PDE backstepping and ODE backstepping is proposed to derive a state‐feedback controller without high differential terms. The well‐posedness and invertibility properties of the PDE backstepping transformation are proved. All states, including coupled linear hyperbolic PDEs and 2 ODEs, are included in the closed‐loop exponential stability analysis. Moreover, boundedness and exponential convergence of the designed controller are proved. The performance is investigated via numerical simulation.