%0 Book Section
%A Lazar, Mircea
%A Heemels, W.P.M.H.
%A Weiland, Siep
%A Bemporad, Alberto
%B American Control Conference
%C 8th-10th June 2005
%D 2005
%F eprints:528
%I IEEE
%K 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
%P 575-580 
%T On the stability of quadratic forms based model predictive control of constrained PWA systems
%U http://eprints.imtlucca.it/528/
%X 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.