Global Finite-Time Stabilization via Time-Varying Feedback for Uncertain Nonlinear Systems

Abstract

This paper focuses on the global finite-time stabilization via time-varying state-feedback for a class of uncertain time-varying nonlinear systems. The problem is rather difficult to solve, mainly due to the presence of more serious unknowns and time-variations and higher nonlinearities in the systems under investigation, particularly those in the control coefficients of the systems. To solve the problem, by skillfully combining time-varying methods and finite-time control theory in the existing literature, a novel time-varying (nonadaptive) design scheme is successfully proposed to finite-time stabilizing controllers. The remarkable feature of the design scheme is the selection of time-varying design functions which can capture the unknowns and time-variations in the systems as time increases. It is shown that if the design parameters and design functions in the designed controller are suitably chosen, then all the signals (i.e., the system states and control input) of the closed-loop system are globally bounded, and furthermore, the system states will reach zero in finite-time and remain zero thereafter. When only unknowns are limited in a known constant interval, a state-feedback controller can be designed to establish the finite-time stability for the resulting closed-loop system. When both unknowns and time-variations are limited in a known constant interval, the global uniform finite-time stability can be established.