Backstepping Control of Linear 2 × 2 Hyperbolic Systems with Dynamic Boundary Conditions. Issue 1 (July 2017) - Deutscher, J.; Gehring, N.; Kern, R.
Abstract: In this paper the boundary control of linear 2 × 2 hyperbolic systems with spatially-varying coefficients and dynamic boundary conditions is considered. This leads to the stabilization problem for a bidirectionally coupled PDE-ODE system. For its solution a two-step backstepping approach is developed, that yields the usual kernel equations and additional decoupling equations of simple form. The latter can be traced back to a Volterra integral equation of the second kind, which is directly solvable with a successive approximation. The results of the paper are illustrated for a heavy rope with load.