### Abstract

Original language | English |
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Title of host publication | Proceedings of the 25th Benelux meeting on Systems and Control, 13-15 March 2006, Heeze, The Netherlands |

Place of Publication | Heeze, Netherlands |

Pages | 43-43 |

Publication status | Published - 2006 |

Event | 25th Benelux Meeting on Systems and Control, March 13-15, 2006, Heeze, The Netherlands - Heeze, Netherlands Duration: 13 Mar 2006 → 15 Mar 2006 |

### Conference

Conference | 25th Benelux Meeting on Systems and Control, March 13-15, 2006, Heeze, The Netherlands |
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Country | Netherlands |

City | Heeze |

Period | 13/03/06 → 15/03/06 |

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### Cite this

*Proceedings of the 25th Benelux meeting on Systems and Control, 13-15 March 2006, Heeze, The Netherlands*(pp. 43-43). Heeze, Netherlands.

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*Proceedings of the 25th Benelux meeting on Systems and Control, 13-15 March 2006, Heeze, The Netherlands.*Heeze, Netherlands, pp. 43-43, 25th Benelux Meeting on Systems and Control, March 13-15, 2006, Heeze, The Netherlands, Heeze, Netherlands, 13/03/06.

**An example of Zero robustness in Piecewise Affine Systems.** / Lazar, M.; Heemels, W.P.M.H.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - An example of Zero robustness in Piecewise Affine Systems

AU - Lazar, M.

AU - Heemels, W.P.M.H.

PY - 2006

Y1 - 2006

N2 - An example is presented in order to illustrate that nominally exponentially stable discrete-time PieceWise Affine (PWA) systems can have zero robustness [1] to arbitrarily small additive disturbances. It is shown that this is mainly due to the absence of a continuous Lyapunov function. The importance of this issue cannot be overstated since nominally stabilizing controllers are affected by perturbations when applied in practice. Moreover, many of the methods for synthesizing stabilizing state-feedback controllers for discrete-time PWA systems employ discontinuous (piecewise quadratic) Lyapunov functions, for example see [2, 3]. The discrete-time input-to-state stability framework [4] is used in order to develop an a posteriori robustness test, which boils down to solving a finite number of linear programming problems. The test can be used to check whether a specific nominally stable PWA system, possibly with a discontinuous Lyapunov function, has some (inherent) robustness to additive disturbances or not.

AB - An example is presented in order to illustrate that nominally exponentially stable discrete-time PieceWise Affine (PWA) systems can have zero robustness [1] to arbitrarily small additive disturbances. It is shown that this is mainly due to the absence of a continuous Lyapunov function. The importance of this issue cannot be overstated since nominally stabilizing controllers are affected by perturbations when applied in practice. Moreover, many of the methods for synthesizing stabilizing state-feedback controllers for discrete-time PWA systems employ discontinuous (piecewise quadratic) Lyapunov functions, for example see [2, 3]. The discrete-time input-to-state stability framework [4] is used in order to develop an a posteriori robustness test, which boils down to solving a finite number of linear programming problems. The test can be used to check whether a specific nominally stable PWA system, possibly with a discontinuous Lyapunov function, has some (inherent) robustness to additive disturbances or not.

M3 - Conference contribution

SN - 978-90-386-2558-4

SP - 43

EP - 43

BT - Proceedings of the 25th Benelux meeting on Systems and Control, 13-15 March 2006, Heeze, The Netherlands

CY - Heeze, Netherlands

ER -