@incollection{eprints740,
            year = {2011},
           title = {Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions},
       booktitle = {Proceedings of the 18th IFAC World Congress},
          author = {Matteo Rubagotti and Sergio Trimboli and Daniele Bernardini and Alberto Bemporad},
          volume = {18},
       publisher = {IFAC},
             url = {http://eprints.imtlucca.it/740/},
        abstract = {For piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set X, this paper proposes a numerical approach to analyze the stability of the origin and to find a region of attraction. The approach relies on introducing fake dynamics outside X and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing X by solving a linear program. The existence of a solution proves that the origin is an asymptotically stable equilibrium of the original PWA system and determines a region of attraction contained in X. The procedure is particularly useful in practical applications for analyzing a posteriori the stability properties of approximate explicit model predictive control laws defined over a bounded set X of states, and to determine whether, for a given set of initial states, the closed-loop system evolves within the domain X where the control law is defined.},
        keywords = {Hybrid systems stability}
}