Second-order nonsingular terminal sliding mode control of uncertain MIMO linear systems

This paper proposes a second-order nonsingular terminal sliding mode control of MIMO uncertain linear systems. In order to design a controller, MIMO systems are converted to 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. A nonsingular terminal sliding mode control law is presented in the paper. The control stratagem can 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. In order to eliminate the chattering of the system, the second-order sliding mode is adopted so as to make the control signal continuous. The simulation results are presented to validate the design.