### Abstract

For piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set χ, 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 χ and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing χ 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 χ. 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 χ 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.

Original language | English |
---|---|

Title of host publication | Proceedings of the 18th IFAC World Congress |

Publisher | IFAC Secretariat |

Pages | 5712-5717 |

Number of pages | 6 |

Volume | 44 |

Edition | 1 PART 1 |

ISBN (Print) | 9783902661937 |

DOIs | |

Publication status | Published - Jan 1 2011 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*Proceedings of the 18th IFAC World Congress*(1 PART 1 ed., Vol. 44, pp. 5712-5717). IFAC Secretariat. https://doi.org/10.3182/20110828-6-IT-1002.00539

**Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions.** / Rubagotti, Matteo; Trimboli, Sergio; Bernardini, Daniele; Bemporad, Alberto.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 18th IFAC World Congress.*1 PART 1 edn, vol. 44, IFAC Secretariat, pp. 5712-5717. https://doi.org/10.3182/20110828-6-IT-1002.00539

}

TY - GEN

T1 - Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions

AU - Rubagotti, Matteo

AU - Trimboli, Sergio

AU - Bernardini, Daniele

AU - Bemporad, Alberto

PY - 2011/1/1

Y1 - 2011/1/1

N2 - For piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set χ, 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 χ and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing χ 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 χ. 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 χ 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.

AB - For piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set χ, 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 χ and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing χ 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 χ. 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 χ 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.

UR - http://www.scopus.com/inward/record.url?scp=84866749126&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866749126&partnerID=8YFLogxK

U2 - 10.3182/20110828-6-IT-1002.00539

DO - 10.3182/20110828-6-IT-1002.00539

M3 - Conference contribution

SN - 9783902661937

VL - 44

SP - 5712

EP - 5717

BT - Proceedings of the 18th IFAC World Congress

PB - IFAC Secretariat

ER -