Lyapunov-stable adaptive stabilization of non-linear time-varying systems with matched uncertainty

This paper considers direct adaptive stabilization of multi-input non-linear time-varying systems with full-state feedback and state-and-time-dependent uncertainty. The novel result of this paper is a single-parameter adaptive controller that yields a Lyapunov-stable closed-loop system. We demonstrate the controller on a non-linear spring-mass-damper, a three-degree-of-freedom Mathieu equation, and a 4th-order non-linear time-varying system.