Robust Fixed-Time Stabilization Control of Generic Linear Systems With Mismatched Disturbances

This article addresses the robust fixed-time stabilization control problem for generic linear systems with both matched and mismatched disturbances. A new observer-based fixed-time control technique is proposed to solve this robust stabilization problem, provided that the system matrix pair $(A,B)$ is controllable. The ultimate boundedness of the closed-loop system in the presence of mismatched disturbances is proven. An upper bound of the convergence time is provided, which is irrelevant to initial conditions. Finally, a simulation example is presented to show the efficiency of the proposed control design method.

I. Introduction

In comparison to asymptotically stable systems, a finite-time stable system exhibits a faster convergence rate, higher accuracy, as well as superior disturbance rejection ability [1]. In particular, the benchmark work [1] provides a Lyapunov stability theorem for establishing finite-time stability of continuous autonomous systems. This motivated many researchers to explore non-Lipschitzian autonomous systems with nonasymptotic convergence properties [2]–[4]. Applications of finite-time stabilization control algorithms to various dynamic systems have been extensively reported as well (see [5]–[10]).