A. J. Koshkouei, K. Burnham and A. S. I. Zinober, “Flatness, Backstepping and Sliding Mode Controllers for Nonlinear Systems,” In: G. Bartolini, L. Fridman, A. Pisano and E. Usai, Eds., Modern Sliding Mode Control Theory, Springer-Verlag, Berlin, 2008, pp. 269-290. doi:10.1007/978-3-540-79016-7_13

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.