Abstract
Control design of a coupled ODE–PDE boundary control system is considered in this paper. The PDE is one dimensional reaction–diffusion equation, with constant parameters, actuated at one of the boundaries and coupled to a linear and time-invariant ODE at the opposite boundary. By introducing a two-step backstepping design procedure, analytic solutions of the kernel and vector-valued functions in the backstepping transformations are obtained. Therefore, a boundary control law in analytic expression is constructed for this coupled ODE–PDE control system.
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