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

Funding information National Basic Research Program of China (973 Program), Grant/Award Number: 2014CB049404; Chongqing University Postgraduates Innovation Project, Grant/Award Number: CYD15023 Summary Motivated 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.

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