Second-order nonsingular terminal sliding mode decomposed control of uncertain multivariable systems

This paper proposes a second-order nonsingular terminal sliding mode decomposed control method for multivariable linear systems with internal parameter uncertainties and external disturbances. First, the systems are converted into the block controllable form, consisting of an input-output subsystem and a stable internal dynamic subsystem. A special second-order nonsingular terminal sliding mode is proposed for the input-output subsystem. The control law is designed to drive the states of the input-output subsystem to converge to the equilibrium point asymptotically. Then the states of the stable zero-dynamics of the system converge to the equilibrium point asymptotically. The method proposed in the paper has advantages for higher-dimensional multivariable systems, in the sense that it simplifies the design and makes it possible to realize a robust decomposed control. Meanwhile, because of the adoption of the second-order sliding mode, the control signal is continuous. Simulation results are presented to validate the design.