Observer‐Based Predefined‐Time Stabilizing Control for Nonlinear Time‐Delay Systems via Dual‐Dynamic‐Gains Method

ABSTRACT This article devotes itself to addressing an observer‐based predefined‐time stabilizing control problem for a nonlinear system subjects to state delays and unavailable states. To realize the state estimation for such a controlled system within a predefined time, an observer is constructed, whose efficiency is relied on the developed dual‐dynamic‐gains. In the foundation of the constructed observer, the predefined‐time and dynamic‐gains‐relied stabilizer is exported under the framework of the backstepping, which enables the formulating closed‐loop system to arrive globally predefined‐time stable, while removing the uncertainties caused by the state delays within a predefined time, which can be demonstrated by the designated Lyapunov‐Krasovskii functionals (L‐K functionals) and homogeneous system theories. In the simulation part of this article, a simulation on the controlled armature motor system is conducted to reflect the availability of the developed control algorithm.