Discretization of control law for a class of variable structure control systems

G. Golo, Arjan van der Schaft, Č. Milosavljević

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    A new method for the discretization of a class of continuous-time variable structure control systems, based on the linear complementarity theory, is proposed. The proposed method consists two steps. In the first step, the motion projected on the sliding manifold (the fast dynamics) is discretized by means of backward Euler time-step method. In the second step, the sampled and hold control law is determined such that the trajectories of the discrete-time closed loop system projected on the sliding manifold coincide with the trajectories of discretized fast dynamics. The discrete-time closed-loop system exhibits discrete-time sliding motion. It means that the trajectories of the discrete-time closed loop system reach the sliding manifold in a finite number of steps and stay on it after that. Also, it is proved that control law is a continuous function. Therefore, the closed loop system is chattering free. The theoretically obtained results are verified on the example of the non-holonomic integrator.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Publication statusPublished - 2000

    Publication series

    NameMemorandum / Faculty of Mathematical Sciences
    PublisherDepartment of Applied Mathematics, University of Twente
    ISSN (Print)0169-2690


    • MSC-74M05
    • MSC-90C33
    • MSC-93C55
    • IR-65738
    • MSC-93C83
    • EWI-3371
    • MSC-93C62

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