Energy-based Control of a Wave Equation with Boundary Anti-damping. Issue 2 (2020) - Macchelli, A.; Gorrec, Y. Le; Wu, Y.; Ramírez, H.
Abstract: In this paper, we consider the asymptotic boundary stabilisation of a one-dimensional wave equation subject to anti-damping at its free end and with control at the opposite one. The control action, implemented through a state feedback or a dynamic controller, is derived by using the port-Hamiltonian framework. More precisely, the standard energy-shaping approach plus damping assignment is adapted to cope with infinite dimensional systems with anti-damping boundary conditions. It is shown how to modify the equivalent dynamic controller to account for the instability propagation along the domain.