Boundary feedback control of an anti-stable wave equation

Abstract

We discuss boundary control of a wave equation with a non-linear anti-damping boundary condition. We design structured finite-dimensional $H_{\infty }$-output feedback controllers which stabilize the infinite dimensional system exponentially in closed loop. The method is applied to control torsional vibrations in drilling systems with the goal to avoid slip-stick.

28 pages, 11 figures, 2 tables