Non‐Uniform Stabilization of a Nonlinear Flexible Marine Riser System With Frictional Damping and Fourier Law

ABSTRACT In this paper, we are considering a new coupled system model, introduced in [Sam et al.,( IEEE Transactions on Control Systems Technology 18, no. 5 (2010) and Wei et al., ( Dynamics and Control of Mechanical Systems in Off Shore Engineering )], called the coupled nonlinear flexible marine riser. We introduce Fourier's law to the model and show that it is well‐posed and exponentially stable with a non‐uniform rate. To do this, since the nonlinearity arising in the model is of the von Kármán type, we use the energy perturbation method to construct a convenient functional equivalent to the energy functional for deriving exponential stability. The result obtained is new and opens a way for applications of thermal law's theory for the new model.