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(eq)X(k) and a discontinuous control U(d) = K(d)X(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.
