@article{eprints1811,
          number = {9},
          author = {Matteo Rubagotti and Sergio Trimboli and Alberto Bemporad},
           title = {Stability and Invariance Analysis of Uncertain Discrete-Time Piecewise Affine Systems},
         journal = {IEEE Transactions on Automatic Control },
           month = {September},
          volume = {58},
       publisher = {IEEE },
           pages = {2359--2365},
            year = {2013},
        keywords = {Model predictive control (MPC); piecewise affine (PWA);   piecewise quadratic (PWQ)
},
        abstract = {This note proposes a method to analyze uniform asymptotic stability and uniform ultimate boundedness of uncertain piecewise affine systems whose dynamics are only defined in a bounded and possibly non-invariant set X of states. The approach relies on introducing fake dynamics outside X and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function via linear programming. The existence of such a function proves stability properties of the original system and allows the determination of a region of attraction contained in X. The procedure is particularly useful in practical applications for analyzing the stability of piecewise affine control systems that are only defined over a bounded subset X of the state space, and to determine whether for a given set of initial conditions the trajectories of the state vector remain within the domain X.},
             url = {http://eprints.imtlucca.it/1811/}
}