Fixed-time stabilization of second-order uncertain multivariable nonlinear systems

This paper studies the fixed-time stabilization problem for a class of second-order multivariable multi-input nonlinear systems with matched uncertainties. Different from the control design for scalar systems, a multivariable sliding mode control design, based on a set of nonlinear coupled sliding surfaces, is proposed to stabilize the system at the origin with a uniformly bounded settling time, i.e., fixed-time stabilization. The key benefit of the proposed design framework is the reduction of discontinuity and singularity. For practical implementation, a saturation function is injected into the proposed design to avoid the control singularity problem, and an almost fixed-time stability of the resultant system is proved by using the phase analysis and the Lyapunov tools. Finally, a two-link planar elbow robot is introduced as an example to validate the effectiveness of our design framework.