On Sliding Control for Multi-Input Multi-Output Nonlinear Systems

Sliding control has been well developed for single-input single-output (SISO) systems, or quasi-SISO systems, in which the sliding condition is a single inequality, or a set of decoupled inequalities. It is also well understood for multiple-input multiple-output (MIMO) systems when certain types of structural information on the dynamics, such as conservation of energy, are available. This paper analyzes, in the general MIMO case, conditions on the system´s parametric uncertainties for the existence of control inputs which keep sliding conditions satisfied. The development is illustrated with a simple example.