Rubagotti, Matteo and Trimboli, Sergio and Bernardini, Daniele and Bemporad, Alberto
*Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions.*
In:
Proceedings of the 18th IFAC World Congress.
IFAC.
ISBN 978-3-902661-93-7
(2011)

## Abstract

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.

Item Type: | Book Section |
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Identification Number: | 10.3182/20110828-6-IT-1002.00539 |

Uncontrolled Keywords: | Hybrid systems stability |

Subjects: | Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery |

Research Area: | Computer Science and Applications |

Depositing User: | Users 37 not found. |

Date Deposited: | 29 Jul 2011 10:52 |

Last Modified: | 30 Sep 2013 12:29 |

URI: | http://eprints.imtlucca.it/id/eprint/740 |

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