TY  - CHAP
ID  - eprints740
T2  - Proceedings of the 18th IFAC World Congress
AV  - none
TI  - Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions
Y1  - 2011///
KW  - Hybrid systems stability
UR  - http://eprints.imtlucca.it/740/
A1  - Rubagotti, Matteo
A1  - Trimboli, Sergio
A1  - Bernardini, Daniele
A1  - Bemporad, Alberto
SN  - 978-3-902661-93-7
PB  - IFAC
N2  - For piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set X, this paper proposes a numerical approach to analyze the stability of the origin and to find a region of attraction. The approach relies on introducing fake dynamics outside X and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing X by solving a linear program. The existence of a solution proves that the origin is an asymptotically stable equilibrium of the original PWA system and determines a region of attraction contained in X. The procedure is particularly useful in practical applications for analyzing a posteriori the stability properties of approximate explicit model predictive control laws defined over a bounded set X of states, and to determine whether, for a given set of initial states, the closed-loop system evolves within the domain X where the control law is defined.
M1  - 18
ER  -