TY  - CHAP
PB  - IEEE
T2  - American Control Conference
Y1  - 2005/06//
SN  - 0-7803-9098-9 
A1  - Lazar, Mircea
A1  - Heemels, W.P.M.H.
A1  - Weiland, Siep
A1  - Bemporad, Alberto
AV  - none
CY  - 8th-10th June 2005
ID  - eprints528
SP  - 575
KW  - 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
UR  - http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1470018&isnumber=31519
N2  - 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.
EP  - 580 
TI  - On the stability of quadratic forms based model predictive control of constrained PWA systems
ER  -