Generalized Homogeneous Unit Control

The methodology of the unit sliding mode control design (known since 1970s) for linear MIMO (Multiply Inputs Multiply Outputs) systems is revised based on the concept of the generalized homogeneity. The conventional restriction about a consistency of the number of control inputs with the dimension of the sliding surface is eliminated. A simple procedure for control parameters tuning is developed. The robustness of the homogeneous unit controller with respect to bounded matched perturbations is proven. The theoretical results are supported by numerical simulations.