### Abstract

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

Pages (from-to) | 4769-4789 |

Number of pages | 21 |

Journal | Nonlinear Analysis: Theory Methods & Applications |

Volume | 71 |

Issue number | 10 |

DOIs | |

Publication status | Published - 15 Nov 2009 |

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### Keywords

- Popov criterion
- Integral control
- Circle criterion
- Infinite-dimensional systems
- Discrete-time systems
- Nonlinear Volterra difference equations
- Absolute stability

### Cite this

**Absolute stability and integral control for infinite-dimensional discrete-time systems.** / Coughlan, J J; Logemann, Hartmut.

Research output: Contribution to journal › Article

*Nonlinear Analysis: Theory Methods & Applications*, vol. 71, no. 10, pp. 4769-4789. https://doi.org/10.1016/j.na.2009.03.072

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TY - JOUR

T1 - Absolute stability and integral control for infinite-dimensional discrete-time systems

AU - Coughlan, J J

AU - Logemann, Hartmut

PY - 2009/11/15

Y1 - 2009/11/15

N2 - We derive absolute stability results of Popov and circle-criterion types for infinite-dimensional discrete-time systems in an input-output setting. Our results apply to feedback systems in which the linear part is the series interconnection of an l(2)-stable linear system and an integrator and the nonlinearity satisfies a sector condition which allows for saturation and deadzone effects. The absolute stability theory is then used to prove tracking and disturbance rejection results for integral control schemes in the presence of input and output nonlinearities. Applications of the input-output theory to state-space systems are also provided.

AB - We derive absolute stability results of Popov and circle-criterion types for infinite-dimensional discrete-time systems in an input-output setting. Our results apply to feedback systems in which the linear part is the series interconnection of an l(2)-stable linear system and an integrator and the nonlinearity satisfies a sector condition which allows for saturation and deadzone effects. The absolute stability theory is then used to prove tracking and disturbance rejection results for integral control schemes in the presence of input and output nonlinearities. Applications of the input-output theory to state-space systems are also provided.

KW - Popov criterion

KW - Integral control

KW - Circle criterion

KW - Infinite-dimensional systems

KW - Discrete-time systems

KW - Nonlinear Volterra difference equations

KW - Absolute stability

UR - http://www.scopus.com/inward/record.url?scp=67651121764&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1016/j.na.2009.03.072

U2 - 10.1016/j.na.2009.03.072

DO - 10.1016/j.na.2009.03.072

M3 - Article

VL - 71

SP - 4769

EP - 4789

JO - Nonlinear Analysis: Theory Methods & Applications

JF - Nonlinear Analysis: Theory Methods & Applications

SN - 0362-546X

IS - 10

ER -