eprintid: 1811
rev_number: 6
eprint_status: archive
userid: 6
dir: disk0/00/00/18/11
datestamp: 2013-09-30 12:23:37
lastmod: 2013-09-30 12:23:37
status_changed: 2013-09-30 12:23:37
type: article
metadata_visibility: show
creators_name: Rubagotti, Matteo
creators_name: Trimboli, Sergio
creators_name: Bemporad, Alberto
creators_id: 
creators_id: 
creators_id: alberto.bemporad@imtlucca.it
title: Stability and Invariance Analysis of Uncertain Discrete-Time Piecewise Affine Systems
ispublished: pub
subjects: TK
divisions: CSA
full_text_status: none
keywords: Model predictive control (MPC); piecewise affine (PWA);   piecewise quadratic (PWQ)

abstract: This note proposes a method to analyze uniform asymptotic stability and uniform ultimate boundedness of uncertain piecewise affine systems whose dynamics are only defined in a bounded and possibly non-invariant set X of states. The approach relies on introducing fake dynamics outside X and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function via linear programming. The existence of such a function proves stability properties of the original system and allows the determination of a region of attraction contained in X. The procedure is particularly useful in practical applications for analyzing the stability of piecewise affine control systems that are only defined over a bounded subset X of the state space, and to determine whether for a given set of initial conditions the trajectories of the state vector remain within the domain X.
date: 2013-09
date_type: published
publication: IEEE Transactions on Automatic Control 
volume: 58
number: 9
publisher: IEEE 
pagerange: 2359-2365
id_number: 10.1109/TAC.2013.2251774
refereed: TRUE
issn: 0018-9286
official_url: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6475975&isnumber=6581905
citation:   Rubagotti, Matteo and Trimboli, Sergio and Bemporad, Alberto  Stability and Invariance Analysis of Uncertain Discrete-Time Piecewise Affine Systems.  IEEE Transactions on Automatic Control , 58 (9).  pp. 2359-2365.  ISSN 0018-9286      (2013)