Variable structure control design on discrete-time systems from another viewpoint

This paper considers the same problem of Furuta (1990) in discrete-time variable structure systems (VSS), but from a different viewpoint. A simple discrete-time variable structure control, which consists of an equivalent control U_eq=K_eqX(k) and a discontinuous control U_d=K_dX(k), is derived to stabilize the system globally. It should be emphasized that the discontinuous feedback gain K_d here is a vector with the same elements; i.e., K_d=k_d[1 1... 1]. The concept of the equilibrium point of the diagonalized system instead of the transformation matrix-T in Furuta (1990) is utilized to determine the switching region. Since the derived switching surface for the control law is not only on the surface s(k)=0, but also in the vicinity of s(k)=0 (i.e., the switching region), the chattering along the sliding mode is reduced explicitly.