Boundary control design for extensible marine risers in three dimensional space

A design of boundary controllers is proposed for (practical) exponential stabilization of extensible marine risers in three-dimensional (3D) space under sea loads. The design removes flaws in existing works. Two Lyapunov-type theorems are developed for study of existence and uniqueness, and stability of nonlinear evolution systems in Hilbert space. These theorems have their potential use in control design and stability analysis for flexible systems including marine risers.