eprintid: 499
rev_number: 9
eprint_status: archive
userid: 7
dir: disk0/00/00/04/99
datestamp: 2011-07-27 09:16:38
lastmod: 2014-07-17 12:21:35
status_changed: 2011-07-27 09:16:38
type: book_section
metadata_visibility: show
item_issues_count: 0
creators_name: Bemporad, Alberto
creators_name: Torrisi, Fabio Danilo
creators_name: Morari, Manfred
creators_id: alberto.bemporad@imtlucca.it
creators_id: 
creators_id: 
title: Optimization-based verification and stability characterization of piecewise affine and hybrid systems
ispublished: pub
subjects: QA75
subjects: TJ
divisions: CSA
full_text_status: none
abstract: In this paper, we formulate the problem of characterizing the stability of a piecewise affine (PWA) system as a verification problem. The basic idea is to take the whole IR n as the set of initial conditions, and check that all the trajectories go to the origin. More precisely, we test for semi-global stability by restricting the set of initial conditions to an (arbitrarily large) bounded set X(0), and label as “asymptotically stable in T steps” the trajectories that enter an invariant set around the origin within a finite time T, or as “unstable in T steps” the trajectories which enter a set X inst of (very large) states. Subsets of X(0) leading to none of the two previous cases are labeled as “non-classifiable in T steps”. The domain of asymptotical stability in T steps is a subset of the domain of attraction of an equilibrium point, and has the practical meaning of collecting the initial conditions from which the settling time to a specified set around the origin is smaller than T. In addition, it can be computed algorithmically in finite time. Such an algorithm requires the computation of reach sets, in a similar fashion as what has been proposed for verification of hybrid systems. In this paper we present a substantial extension of the verification algorithm presented in [6] for stability characterization of PWA systems, based on linear and mixed-integer linear programming. As a result, given a set of initial conditions we are able to determine its partition into subsets of trajectories which are asymptotically stable, or unstable, or non-classifiable in T steps. 
date: 2000
date_type: published
series: Lecture Notes in Computer Science
publication: Hybrid Systems: Computation and Control
volume: 1790
publisher: Springer-Verlag
pagerange: 45-58
id_number: 10.1007/3-540-46430-1_8
refereed: TRUE
isbn:     978-3-540-67259-3
book_title: Hybrid Systems: Computation and Control
editors_name: Lynch, Nancy
editors_name: Krogh, Bruce
official_url: http://dx.doi.org/10.1007/3-540-46430-1_8
citation:   Bemporad, Alberto and Torrisi, Fabio Danilo and Morari, Manfred  Optimization-based verification and stability characterization of piecewise affine and hybrid systems.   In:  Hybrid Systems: Computation and Control.   Lecture Notes in Computer Science, 1790 .  Springer-Verlag, pp. 45-58.  ISBN  978-3-540-67259-3      (2000)