@article{eprints473,
           title = {On hybrid systems and closed-loop MPC systems},
          volume = {47},
       publisher = {IEEE},
           pages = {863--869},
          author = {Alberto Bemporad and W.P.M.H. Heemels and Bart De Schutter},
          number = {5},
            year = {2002},
           month = {May},
         journal = {IEEE Transactions on Automatic Control},
        abstract = {The following five classes of hybrid systems were recently proven to be equivalent: linear complementarity, extended linear complementarity, mixed logical dynamical systems, piecewise affine systems and max-min-plus-scaling systems. Some of the equivalences were obtained under additional assumptions, such as boundedness of certain system variables. In this paper, for linear or hybrid plants in closed-loop with a model predictive control (MPC)controller based on a linear model fulfilling linear constraints on input and state variables and utilizing a quadratic cost criterion, we provide a simple and direct proof that the closed-loop system is a subclass of any of the former five classes of hybrid systems. This result is of extreme importance, as it opens up the use of tools developed for the mentioned hybrid model classes, such as (robust) stability and safety analysis tools, to study closed-loop properties of MPC},
             url = {http://eprints.imtlucca.it/473/},
        keywords = {bounded system variables; closed-loop model predictive control systems; equivalent systems; hybrid systems; input variables; linear complementarity; linear constraints; linear model; linear plants; max-min-plus-scaling systems; mixed analogue/logical systems; mixed continuous/discrete systems;mixed logical dynamical systems;piecewise affine systems; quadratic cost criterion; robust stability; safety analysis tools; state variables; closed loop systems; discrete systems; linear systems; predictive control; safety; stability}
}