# Analysis, design, and performance limitations of $H_{\infty}$ optimal filtering in the presence of an additional input with known frequency

Ali Saberi, Antonie Arij Stoorvogel, Peddapullaiah Sannuti

1 Citation (Scopus)

### Abstract

A generalized $\gamma$-level $H_\infty$ sub-optimal input decoupling (SOID) filtering problem is formulated. It is a generalization of $\gamma$-level $H_\infty$ SOID filtering problem when, besides an input with unknown statistical properties but with a finite RMS norm, there exists an additional input to the given plant or system. The additional input is a linear combination of sinusoidal signals each of which has an unknown amplitude and phase but known frequency. The analysis, design, and performance limitations of generalized $H_\infty$ optimal filters are presented.
Original language Undefined 10.1002/rnc.1182 1474-1488 15 International journal of robust and nonlinear control 17 LNCS4549/16 https://doi.org/10.1002/rnc.1182 Published - 2007

### Keywords

• EWI-11069
• METIS-241913
• IR-61919

### Cite this

@article{038c3acf2ac040a39afa730b9ea7ea99,
title = "Analysis, design, and performance limitations of $H_{\infty}$ optimal filtering in the presence of an additional input with known frequency",
abstract = "A generalized $\gamma$-level $H_\infty$ sub-optimal input decoupling (SOID) filtering problem is formulated. It is a generalization of $\gamma$-level $H_\infty$ SOID filtering problem when, besides an input with unknown statistical properties but with a finite RMS norm, there exists an additional input to the given plant or system. The additional input is a linear combination of sinusoidal signals each of which has an unknown amplitude and phase but known frequency. The analysis, design, and performance limitations of generalized $H_\infty$ optimal filters are presented.",
keywords = "EWI-11069, METIS-241913, IR-61919",
author = "Ali Saberi and Stoorvogel, {Antonie Arij} and Peddapullaiah Sannuti",
note = "10.1002/rnc.1182",
year = "2007",
doi = "10.1002/rnc.1182",
language = "Undefined",
volume = "17",
pages = "1474--1488",
journal = "International journal of robust and nonlinear control",
issn = "1049-8923",
publisher = "Wiley",
number = "LNCS4549/16",

}

In: International journal of robust and nonlinear control, Vol. 17, No. LNCS4549/16, 10.1002/rnc.1182, 2007, p. 1474-1488.

TY - JOUR

T1 - Analysis, design, and performance limitations of $H_{\infty}$ optimal filtering in the presence of an additional input with known frequency

AU - Saberi, Ali

AU - Stoorvogel, Antonie Arij

AU - Sannuti, Peddapullaiah

N1 - 10.1002/rnc.1182

PY - 2007

Y1 - 2007

N2 - A generalized $\gamma$-level $H_\infty$ sub-optimal input decoupling (SOID) filtering problem is formulated. It is a generalization of $\gamma$-level $H_\infty$ SOID filtering problem when, besides an input with unknown statistical properties but with a finite RMS norm, there exists an additional input to the given plant or system. The additional input is a linear combination of sinusoidal signals each of which has an unknown amplitude and phase but known frequency. The analysis, design, and performance limitations of generalized $H_\infty$ optimal filters are presented.

AB - A generalized $\gamma$-level $H_\infty$ sub-optimal input decoupling (SOID) filtering problem is formulated. It is a generalization of $\gamma$-level $H_\infty$ SOID filtering problem when, besides an input with unknown statistical properties but with a finite RMS norm, there exists an additional input to the given plant or system. The additional input is a linear combination of sinusoidal signals each of which has an unknown amplitude and phase but known frequency. The analysis, design, and performance limitations of generalized $H_\infty$ optimal filters are presented.

KW - EWI-11069

KW - METIS-241913

KW - IR-61919

U2 - 10.1002/rnc.1182

DO - 10.1002/rnc.1182

M3 - Article

VL - 17

SP - 1474

EP - 1488

JO - International journal of robust and nonlinear control

JF - International journal of robust and nonlinear control

SN - 1049-8923

IS - LNCS4549/16

M1 - 10.1002/rnc.1182

ER -