New Results on Fixed-Time Stabilization of Switched Uncertain Nonlinear Systems in p-Normal Form

Abstract

In this article, the global fixed-time stabilization problem is addressed for a class of switched uncertain nonlinear systems in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -normal form. Different from the existing results, the bounds of the unknown system parameters, including dead-zone parameters and control coefficients, are not required to be known. By combining the adding a power integrator technique with the common Lyapunov function method, a novel adaptive controller is proposed and a dynamic controller parameter is introduced to cope with the unknown system parameters. Besides, an effective common regulate rule is designed based on the improved fixed-time stability framework. Furthermore, it is shown that the controller parameter can be regulated online by the switching mechanism to compensate the unknown system parameters and the system states can converge to zero in fixed time under arbitrary switchings. The effectiveness of the proposed method is verified by a simulation example.