Multivariable second order sliding mode control of mechanical systems

The paper proposes an approach to second order sliding mode control for multi-input multi-output (MIMO) nonlinear uncertain systems. With respect to standard sliding mode control, the second order sliding mode techniques for single-input single-output (SISO) systems show the same properties of robustness and precision, feature a higher order accuracy and can be exploited to eliminate the chattering effect. The extension of these results to the MIMO nonlinear systems is a challenging matter. In the present paper, the validity is extended to a quite large class of nonlinear processes affected by uncertainties of general nature; the control design is simple; the conditions of existence on the controllers are weak. The proposed procedure, which represents a general approach to the second order sliding mode control of MIMO systems, is applied to the control of mechanical systems.