Study On Stabilization Of High Order Delay Feedforward Nonlinear System

As is well-known, adding a power integrator method e?ectively solves the feedback controll problem of higher-order nonlinear systems. By combining the other approaches,such as the saturation control strategy, the homogeneous dominant method and stability theory, it also resolves the stabilization problem and tracking control problem for highorder feedforward nonlinear systems.On the other hand, Time-delay and uncertainty phenomenon usually occurs in the real control system. Ignoring their impact will result in system instability or performance deterioration. For the specific system, time-delay and uncertainty may exist in the state or control input. Therefore, this paper will study the problem of global stabilization for two classes of high-order feedforward time-delay nonlinear systems. The main contributions include the following two parts.1. Global state-feedback stabilization for a class of high-order feedforward nonlinear systems with time-delay states.This part addresses the problem of global state-feedback stabilization for a class of high-order feedforward nonlinear systems with time-delay states. Based on adding a power integrator approach, the homogeneous domination method, Lyapunov-Razumikhin function idea, we design a global stabilizer by the introduce of sign functions and saturation functions, which guarantees the globally asymptotic stability of the closed-loop systems.2. Global output-feedback stabilization for a class of high-order feedforward nonlinear systems with state delay and input delay.This part investigates the output-feedback stabilization problem for a class of highorder feedforward nonlinear systems with state delay and input delay. Under a weaken assumption that the powers of nonlinear functions are relaxed to an interval, the new control strategy implanting sign functions into homogeneous domination idea and observer construction allows time-varying delays to coexist in system state and control input. With the aid of delicate selections of design parameters, observer gains and Lyapunov-Krasovskii functionals, it is shown that the closed-loop system is globally asymptotically stable.