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S. V. Emeyanov and V. A. Taran, “On One Class of Variable Structure Control Systems,” Computational Mathematics and Modeling, Vol. 21, No. 3, 2006, pp. 5-26.

has been cited by the following article:

• TITLE: Embedding-Based Sliding Mode Control for Linear Time Varying Systems

  AUTHORS: Mohammad Reza Zarrabi, Mohammad Hadi Farahi, Ali Jafar Koshkouei, Sohrab Effati, Keith Burnham

  KEYWORDS: Time Optimal Control Problem, Measure Theory, Sliding Mode Control, Sliding Surface Design, Equivalent Control

  JOURNAL NAME: Applied Mathematics, Vol.2 No.4, March 31, 2011

  ABSTRACT: In this paper, a novel strategy using embedding process and sliding surface is proposed. In this method, a state trajectory starting from a given initial point reaches a definite point on a sliding surface in the minimum time, and then tends to the origin along the sliding surface (SS). In the first, a SS is designed, then using an appropriate measure, an embedding is constructed to solve a time optimal control problem such that the system trajectory reaches the SS in minimum time, after that a control is designed such that the system trajectory tends to the origin along the SS. It is well-known that the main disadvantage of the use of sliding mode controls (SMCs) is a phenomenon, the so-called chattering. The proposed SMC here is piecewise continuous and chattering free. Some numerical examples is presented to illustrate the effectiveness and reliability of the proposed method.