Second-order sliding mode control for high-dimension uncertain multivariable systems

A second-order non-singular terminal sliding mode (NTSM) controller with hierarchical structure, is proposed for a class of uncertain high-dimensional multivariable systems. By two non-singular state transformations, the system is firstly converted into decomposed block controllable form, consisting of an input-output subsystem and an internal one. A second-order NTSM controller is designed to force the input-output subsystem to converge to zero with characteristics of fast and better tracking precision, as well as free-chattering. Meanwhile, the internal subsystem is converted into zero dynamic subsystem, which asymptotical stability and finally that of the original system is guaranteed by eigenvalue configuration method. The simulation results are presented to validate the designed method.