Global state feedback stabilization of nonlinear systems with unknown functions

This paper studies the global state feedback stabilization problem of nonlinear systems with unknown functions. Firstly, in order to deal with the problem of unknown functions, a Lemma is proposed and proved. The assumption of unknown function is avoided, so the conservatism is reduced. Secondly, based on Lyapunov analysis and backstepping method, a global stabilization control algorithm for systems with unknown functions is proposed. The algorithm does not use adaptive control method, so the control scheme is relatively simple. Finally, in order to verify the effectiveness, the proposed algorithm is applied to the stabilization problem of a single-link robot and Chua’s oscillator system.