## Optimization-Based Verification and Stability Characterization of Piecewise Affine and Hybrid Systems (2000)

Venue: | In Hybrid Systems: Computation and Control |

Citations: | 29 - 8 self |

### BibTeX

@INPROCEEDINGS{Bemporad00optimization-basedverification,

author = {Alberto Bemporad and Fabio Danilo Torrisi and Manfred Morari},

title = {Optimization-Based Verification and Stability Characterization of Piecewise Affine and Hybrid Systems},

booktitle = {In Hybrid Systems: Computation and Control},

year = {2000},

pages = {45--58},

publisher = {Springer Verlag}

}

### OpenURL

### Abstract

In this paper, we formulate the problem of characterizing the stability of a piecewise affin (PWA) system as a verification problem. The basic idea is to take the whole R^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 in variant set around the origin within a finite time T ,or as "unstable in T steps" the trajectories which enter a (very large) set X_inst . Subsets of X (0) leadin ton2W of the two previous cases are labeled as "nv classifiable in T steps". The domain of asymptotical stability in T steps is a subset of the domain of attraction ofan equilibrium poin t, an has the practicalmeanca of collectin inPv)v convW2xvP from which the settlin time of the system is smaller than T . In addition it can be computed algorithmically i...