Fixed-time Output Feedback Stabilization and Settling Time Analysis for High-Order Integrator Systems

This paper presents a method for stabilizing a high-order integrator system in a fixed time by output feedback control. First, we propose a state observer for a high-order integrator system that can achieve the real states within a fixed time regardless of the volume of initial errors. We determine the upper bound of the settling time for the observer to achieve real states, which helps in estimating the settling time of the entire stabilization process. In addition, we establish a fixed-time output feedback control law by employing the homogeneity technique to achieve fixed-time stability. Furthermore, it is worth mentioning that there is a certain conservatism in the existing estimations of the settling time of higher-order integrator systems. This study proposes an indirect method to improve the settling time estimation process by constructing a new system. In addition, we present a numerical example to illustrate the effectiveness of the proposed method.