### Abstract

A recursive robust H_{∞} filtering algorithm is newly proposed for the discrete time uncertain linear system subject to the energy constraint called sum quadratic constraint (SQC). A set valued estimation approach will be used to tackle the given problem. To this end, by combining an SQC on the H_{∞} norm condition of the error dynamics and an inequality relationship between the uncertainty input and output, we obtain an augmented SQC and then formulate the robust H_{∞}, filtering problem as the one of finding the set of estimates satisfying this constraint. The solutions will be given in terms of ellipsoids whose centers are the minimums of the indefinite quadratic function defined by the augmented SQC. The Krein space estimation theory will be utilized to efficiently deal with the minimization problem of the indefinite quadratic function and it is shown that the robust H_{∞} filter turns out to be just the special form of Krein space Kalman filter. The proposed robust filter has basically the same recursive structure as the information form of Kalman filter and therefore demands less computational burdens for the implementation. Numerical examples will be given to verify that the proposed filter guarantees the robustness in the presence of parametric uncertainties and its bounding ellipsoidal sets of filtered estimates always contain true states.

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

Pages (from-to) | 5182-5187 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 5 |

Publication status | Published - 2004 Dec 1 |

Event | 2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas Duration: 2004 Dec 14 → 2004 Dec 17 |

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### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization

### Cite this

_{∞}filtering within the framework of set-valued estimation.

*Proceedings of the IEEE Conference on Decision and Control*,

*5*, 5182-5187.

}

_{∞}filtering within the framework of set-valued estimation',

*Proceedings of the IEEE Conference on Decision and Control*, vol. 5, pp. 5182-5187.

**Recursive robust H _{∞} filtering within the framework of set-valued estimation.** / Ra, Won Sang; Jin, Seung Hee; Yoon, Tae Sung; Park, Jin Bae.

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - Recursive robust H∞ filtering within the framework of set-valued estimation

AU - Ra, Won Sang

AU - Jin, Seung Hee

AU - Yoon, Tae Sung

AU - Park, Jin Bae

PY - 2004/12/1

Y1 - 2004/12/1

N2 - A recursive robust H∞ filtering algorithm is newly proposed for the discrete time uncertain linear system subject to the energy constraint called sum quadratic constraint (SQC). A set valued estimation approach will be used to tackle the given problem. To this end, by combining an SQC on the H∞ norm condition of the error dynamics and an inequality relationship between the uncertainty input and output, we obtain an augmented SQC and then formulate the robust H∞, filtering problem as the one of finding the set of estimates satisfying this constraint. The solutions will be given in terms of ellipsoids whose centers are the minimums of the indefinite quadratic function defined by the augmented SQC. The Krein space estimation theory will be utilized to efficiently deal with the minimization problem of the indefinite quadratic function and it is shown that the robust H∞ filter turns out to be just the special form of Krein space Kalman filter. The proposed robust filter has basically the same recursive structure as the information form of Kalman filter and therefore demands less computational burdens for the implementation. Numerical examples will be given to verify that the proposed filter guarantees the robustness in the presence of parametric uncertainties and its bounding ellipsoidal sets of filtered estimates always contain true states.

AB - A recursive robust H∞ filtering algorithm is newly proposed for the discrete time uncertain linear system subject to the energy constraint called sum quadratic constraint (SQC). A set valued estimation approach will be used to tackle the given problem. To this end, by combining an SQC on the H∞ norm condition of the error dynamics and an inequality relationship between the uncertainty input and output, we obtain an augmented SQC and then formulate the robust H∞, filtering problem as the one of finding the set of estimates satisfying this constraint. The solutions will be given in terms of ellipsoids whose centers are the minimums of the indefinite quadratic function defined by the augmented SQC. The Krein space estimation theory will be utilized to efficiently deal with the minimization problem of the indefinite quadratic function and it is shown that the robust H∞ filter turns out to be just the special form of Krein space Kalman filter. The proposed robust filter has basically the same recursive structure as the information form of Kalman filter and therefore demands less computational burdens for the implementation. Numerical examples will be given to verify that the proposed filter guarantees the robustness in the presence of parametric uncertainties and its bounding ellipsoidal sets of filtered estimates always contain true states.

UR - http://www.scopus.com/inward/record.url?scp=14544277164&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14544277164&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:14544277164

VL - 5

SP - 5182

EP - 5187

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -

_{∞}filtering within the framework of set-valued estimation. Proceedings of the IEEE Conference on Decision and Control. 2004 Dec 1;5:5182-5187.