Homogeneous Unit Sliding Mode Control

The methodology of the unit sliding mode control design (known since 1970s) for linear systems is revised based on the concept of the generalized homogeneity. The restriction about a consistency of the number of control inputs with the dimension of the sliding surface is eliminated. A simple procedure of control parameters tuning based on a known maximal magnitude of matched perturbations is developed. To deal with perturbations of unknown magnitude, a homogeneous sliding mode control with integral action is designed as well. The theoretical results are supported by numerical simulations.