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.
2016 35th Chinese Control Conference (CCC)