### Abstract

We present a conic sector theorem for linear parameter varying (LPV) systems in which the traditional definition of conicity is violated for certain values of the parameter. We show that such LPV systems can be defined to be conic in an average sense if the parameter trajectories are restricted so that the system operates with such values of the parameter sufficiently rarely. We then show that such an average definition of conicity is useful in analyzing the stability of the system when it is connected in feedback with a conic system with appropriate conic properties. This can be regarded as an extension of the classical conic sector theorem. Based on this modified conic sector theorem, we design conic controllers that allow the closedloop system to operate in nonconic parameter regions for brief periods of time. Due to this extra degree of freedom, these controllers lead to less conservative performance than traditional designs, in which the controller parameters are chosen based on the largest cone that the plant dynamics are contained in. We demonstrate the effectiveness of the proposed design in stabilizing a power grid with very high penetration of renewable energy while minimizing power transmission losses.

Original language | English (US) |
---|---|

Pages (from-to) | 224-229 |

Number of pages | 6 |

Journal | IEEE Control Systems Letters |

Volume | 2 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2018 |

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### Keywords

- Linear parameter-varying systems
- Power systems
- Time-varying systems

### Cite this

*IEEE Control Systems Letters*,

*2*(2), 224-229. https://doi.org/10.1109/LCSYS.2018.2807483

**Conic-sector-based analysis and control synthesis for linear parameter varying systems.** / Sivaranjani, S.; Forbes, James Richard; Seiler Jr, Peter J; Gupta, Vijay.

Research output: Contribution to journal › Article

*IEEE Control Systems Letters*, vol. 2, no. 2, pp. 224-229. https://doi.org/10.1109/LCSYS.2018.2807483

}

TY - JOUR

T1 - Conic-sector-based analysis and control synthesis for linear parameter varying systems

AU - Sivaranjani, S.

AU - Forbes, James Richard

AU - Seiler Jr, Peter J

AU - Gupta, Vijay

PY - 2018/4/1

Y1 - 2018/4/1

N2 - We present a conic sector theorem for linear parameter varying (LPV) systems in which the traditional definition of conicity is violated for certain values of the parameter. We show that such LPV systems can be defined to be conic in an average sense if the parameter trajectories are restricted so that the system operates with such values of the parameter sufficiently rarely. We then show that such an average definition of conicity is useful in analyzing the stability of the system when it is connected in feedback with a conic system with appropriate conic properties. This can be regarded as an extension of the classical conic sector theorem. Based on this modified conic sector theorem, we design conic controllers that allow the closedloop system to operate in nonconic parameter regions for brief periods of time. Due to this extra degree of freedom, these controllers lead to less conservative performance than traditional designs, in which the controller parameters are chosen based on the largest cone that the plant dynamics are contained in. We demonstrate the effectiveness of the proposed design in stabilizing a power grid with very high penetration of renewable energy while minimizing power transmission losses.

AB - We present a conic sector theorem for linear parameter varying (LPV) systems in which the traditional definition of conicity is violated for certain values of the parameter. We show that such LPV systems can be defined to be conic in an average sense if the parameter trajectories are restricted so that the system operates with such values of the parameter sufficiently rarely. We then show that such an average definition of conicity is useful in analyzing the stability of the system when it is connected in feedback with a conic system with appropriate conic properties. This can be regarded as an extension of the classical conic sector theorem. Based on this modified conic sector theorem, we design conic controllers that allow the closedloop system to operate in nonconic parameter regions for brief periods of time. Due to this extra degree of freedom, these controllers lead to less conservative performance than traditional designs, in which the controller parameters are chosen based on the largest cone that the plant dynamics are contained in. We demonstrate the effectiveness of the proposed design in stabilizing a power grid with very high penetration of renewable energy while minimizing power transmission losses.

KW - Linear parameter-varying systems

KW - Power systems

KW - Time-varying systems

UR - http://www.scopus.com/inward/record.url?scp=85057638099&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057638099&partnerID=8YFLogxK

U2 - 10.1109/LCSYS.2018.2807483

DO - 10.1109/LCSYS.2018.2807483

M3 - Article

VL - 2

SP - 224

EP - 229

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

SN - 2475-1456

IS - 2

ER -