Global adaptive stabilization for high-order uncertain time-varying nonlinear systems with time-delays

This paper focuses on the adaptive stabilization problem for a class of high-order nonlinear systems with time-varying uncertainties and unknown time-delays. Time-varying uncertain parameters are compensated by combining a function gain with traditional adaptive technique, and unknown multiple time-delays are manipulated by the delicate choice of an appropriate Lyapunov function. With the help of homogeneous domination idea and recursive design, a continuous adaptive state-feedback controller is designed to guarantee that resulting closed-loop systems are globally uniformly stable and original system states converge to zero. The effectiveness of the proposed control scheme is illustrated by the stabilization of delayed neural network systems. Copyright (c) 2016 John Wiley & Sons, Ltd.