Global Output-feedback Stabilization for Nonlinear Time-delay Systems with Unknown Control Coefficients

This paper investigates the problem of global stabilization by output-feedback for a class of planar nonlinear systems with unknown time-delay and control coefficients. Compared with the closely related works, the highlight of the paper is that it is not required that the upper and lower bounds of unknown control coefficients are known a prior, and meanwhile, the derivative of unknown time-varying time-delay is also not required to have known upper bound. This makes the problem essentially different, and much more difficult to solve. Motivated by our recent works, by combining the method of universal control with backstepping technique, and skillfully constructing a new Lyapunov-Krasoviskii functional, we design a new adaptive stabilizing controller with the suitable design parameters which guarantees that the resulting closed-loop system state is globally bounded while the state of the original system converges to the origin after a finite time. A numerical example is given to illustrate the effectiveness of the theoretical results.