Discrete second order sliding mode control for nondecouplable multivariable systems via input-output model

In this work, a robust discrete second order sliding mode control (2-DSMC) via input-output model for multivariable systems was proposed. Firstly, a discrete second order sliding mode control for decouplable multivariable systems was presented. Then, a robust discrete second order sliding mode control for nondecouplable multivariable systems was developed. The synthesis of the last proposed control law needed the use of a polynomial matrix called interactor matrix. A numerical example proved that very satisfactory performances were recorded in terms of reducing the chattering phenomenon using new discrete second order sliding mode control for nondecouplable multivariable (MIMO) systems.