%0 Book Section
%A Bemporad, Alberto
%A Heemels, W.P.M.H.
%A De Schutter, Bart
%B Decision and Control Conference
%C Orlando, Florida USA, December 2001
%D 2001
%F eprints:584
%I IEEE
%K bounded system variables; closed-loop system; equivalences; hybrid plants; hybrid systems; input variables; linear complementarity systems; linear constraints;linear model;linear plants; max-min-plus-scaling systems; mixed logical-dynamical systems; model predictive control; piecewise affine systems; robust stability; safety analysis; state variables; closed loop systems; predictive control; safety; stability
%P 1645-1650
%T On hybrid systems and closed-loop MPC systems
%U http://eprints.imtlucca.it/584/
%V 2
%X The following five classes of hybrid systems were proved by W.P.M.H. Heemels et al. (2001) to be equivalent: linear complementarity (LC) systems, extended linear complementarity (ELC) systems, mixed logical-dynamical (MLD) systems, piecewise affine (PWA) systems and max-min-plus-scaling (MMPS) systems. Some of the equivalences were obtained under additional assumptions, such as boundedness of system variables. In this paper, for closed-loop linear or hybrid plants with model-predictive control (MPC) based on a linear model and fulfilling linear constraints on the input and state variables, we provide a simple and direct proof that the closed-loop system (cl-MPC) is a subclass of any of the former five classes of hybrid systems. This result opens up the use of tools developed for hybrid systems (such as stability, robust stability and safety analysis tools) to study the closed-loop properties of MPC