TY  - CHAP
ED  - Lynch, Nancy
ED  - Krogh, Bruce
SP  - 45
T3  - Lecture Notes in Computer Science
A1  - Bemporad, Alberto
A1  - Torrisi, Fabio Danilo
A1  - Morari, Manfred
PB  - Springer-Verlag
Y1  - 2000///
T2  - Hybrid Systems: Computation and Control
EP  - 58
ID  - eprints499
M1  - 1790
N2  - 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. 
SN  -     978-3-540-67259-3
UR  - http://dx.doi.org/10.1007/3-540-46430-1_8
TI  - Optimization-based verification and stability characterization of piecewise affine and hybrid systems
AV  - none
ER  -