Performance output tracking and disturbance rejection for one-dimensional wave equation with boundary disturbance

This paper is concerned with output reference signal tracking and disturbance rejection for one dimensional wave equation. We first design a state reference system determined by the reference signal. Then based on Lyapunov functional method, we design a variable structure performance output tracking controller. Four control objectives are achieved: a) the output is tracking the reference signal ;b) the external disturbance is rejected ; c) all the internal-loops are bounded; d) when the disturbance and reference are disconnected, the closed-loop is exponentially stable. Finally, the state of the system is shown to be tracking the reference state.