%0 Book Section
%A Lazar, Mircea
%A Heemels, W.P.M.H.
%A Weiland, Siep
%A Bemporad, Alberto
%B Decision and Control Conference
%C 14th-17th December 2004
%D 2004
%F eprints:521
%I IEEE
%K constrained piecewise affine systems; constraint set method; linear matrix inequalities; model predictive control; positively invariant sets; semidefinite programming; stabilization conditions; terminal cost; linear matrix inequalities; mathematical programming; predictive control; set theory; stability
%P 4595-4600
%T Stabilization conditions for model predictive control of constrained PWA systems
%U http://eprints.imtlucca.it/521/
%V 5
%X Model predictive control (MPC) has recently been applied to several relevant classes of hybrid systems with promising results. These developments generated an increasing interest towards issues such as stability and computational problems that arise in hybrid MPC. Stability aspects have been addressed only marginally. In this paper we present an extension of the terminal cost and constraint set method for guaranteeing stability in MPC to the class of constrained piecewise affine systems. Semidefinite programming is used to calculate the employed terminal weight matrix that ensures stability for quadratic cost based MPC. A procedure for computing a robust positively invariant set for piecewise linear systems is also developed. The implementation of the proposed method is illustrated by an example.