Adaptive stabilization of linear second-order systems with bounded time-varying coefficients

We consider adaptive stabilization for a class of linear time-varying second-order systems. Interpreting the system states as position and velocity, the system is assumed to have unknown, non-parametric, bounded time-varying damping and stiffness coefficients. The coefficient bounds need not be known to implement the adaptive controller. Lyapunov methods are used to prove global convergence of the system states. For illustration, the controller is used to stabilize several example systems.