Robust Stabilization of Time-Varying Nonlinear Systems With Time-Varying Delays: A Fully Actuated System Approach

A general time-varying nonlinear uncertain system with time-varying delays is proposed, which is composed of two subsystems: one is an uncertain fully actuated subsystem representing the controllable part in the system, the other is an isolated globally uniformly asymptotically (GUA) stable autonomous subsystem which represents the uncontrollable part in the system. Both the single-order fully actuated system (FAS) and the multiorder FAS representations of the controllable subsystem are introduced. The problem of robust stabilization of such a compound system with full-state feedback can be converted into an input-to-state GUA stabilization problem of the fully actuated subsystem, which is solved for both types of single- and multiorder FASs with very general assumptions on the uncertain perturbed functions. Under certain conditions, the solution reduces to that for robust stabilization with partial-state feedback, and naturally reduce to that for robust stabilization of FASs. Two illustrative examples demonstrate both the effect and the application procedure of the proposed robust stabilization approach.