Local exponential stabilization of a coupled burgers' PDE-ODE system

This paper concerns the boundary stabilization problem of a coupled system consisting of the Burgers' equation and a linear ordinary differential equation (ODE). The Burgers' equation is a widely considered nonlinear partial differential equation (PDE), partially due to its low order and partially due to its structure analogous to the Navier-Stokes equation which describes fluid dynamics. The controller we employ for stabilizing this nonlinear coupled system was firstly developed from the boundary control problem of the corresponding linearized system, based on an infinite-dimensional backstepping transformation. By construction of a strict Lyapunov functional, the closed-loop nonlinear system with the backstepping controller is proved to be locally exponentially stable.