## Abstract

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.

Original language | English |
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Pages (from-to) | 1-16 |

Number of pages | 16 |

Journal | Control, theory and advanced technology |

Volume | 8 |

Issue number | 1 |

State | Published - Mar 1992 |