Adaptive Stabilization of Feedforward Time-delay Systems with Uncertain Output Equation

In this work, the problem of global adaptive stabilization is solved by output feedback for a family of feedforward nonlinear time-delay systems with uncertain output equation and unknown growth rate. To deal with system uncertainty, a low-gain observer incorporating with novel adaptive gain is first proposed. Next, via output feedback, an adaptive delay-free controller is constructed by combining scaling change with backstepping algorithm. Compared with existing results, the controller proposed is capable of handling both uncertain output equation and unknown delay. With the aid of Lyapunov-Krasovskii functional and Barbalat's lemma, it is shown that the state and its estimate converge asymptotically to zero, and the adaptive gain is bounded. Furthermore, by numerical simulations, the usefulness of the control scheme is illustrated.