Nonsmooth Feedback Adaptive Stabilization for High-Order Nonlinear Systems Subject to State Delay

This paper proposes a nonsmooth control scheme for high-order nonlinear time-delay systems without extra assumptions, which can be regarded as an expansion of the backstepping method based on dynamic gains. With the help of the Lyapunov-Krasovskii theorem, a continuous and memoryless controller is explicitly constructed, which guarantees that all the closed-loop signals are globally uniformly ultimately bounded while the original system states asymptotically converge to zero. Finally, an example is given to illustrate the usefulness of our result.