@incollection{eprints528,
           pages = {575--580 },
       publisher = {IEEE},
       booktitle = {American Control Conference},
          author = {Mircea Lazar and W.P.M.H. Heemels and Siep Weiland and Alberto Bemporad},
            year = {2005},
         journal = {American Control Conference},
         address = {8th-10th June 2005},
           title = {On the stability of quadratic forms based model predictive control of constrained PWA systems},
           month = {June},
        keywords = {Lyapunov function; Lyapunov stability; S-procedure technique; asymptotic stability; closed-loop system; constrained PWA systems; constraint set method; discrete-time PWA systems; hybrid systems; linear matrix inequalities; mixed integer quadratic programming problem; model predictive control; online optimization problem; piecewise affine systems; piecewise polyhedral positively invariant sets; quadratic cost; quadratic forms; terminal cost method; Lyapunov methods; asymptotic stability; discrete time systems; integer programming; linear matrix inequalities; piecewise polynomial techniques; predictive control; quadratic programming},
        abstract = {In this paper we investigate the stability of discrete-time PWA systems in closed-loop with quadratic cost based Model Predictive Controllers (MPC) and we derive a priori sufficient conditions for Lyapunov asymptotic stability.
We prove that Lyapunov stability can be achieved for the
closed-loop system even though the considered Lyapunov
function and the system dynamics may be discontinuous.
The stabilization conditions are derived using a terminal
cost and constraint set method. An S-procedure technique
is employed to reduce conservativeness of the stabilization
conditions and a linear matrix inequalities set-up is developed in order to calculate the terminal cost. A new algorithm for computing piecewise polyhedral positively invariant sets for PWA systems is also presented. In this manner, the on-line optimization problem associated with MPC leads to a mixed integer quadratic programming problem, which can be solved by standard optimization tools.},
             url = {http://eprints.imtlucca.it/528/}
}