<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper the explicit necessary and sufficient conditions for the existence of Luenberger reduced order observer are established. In particular, it is proven that for the given linear time-invariant system of order <italic>n</italic>, having <italic>p</italic> linearly independent outputs and <italic>m</italic> inputs, a Luenberger observer of order (<italic>n</italic> − <italic>p</italic>) can be constructed if and only if the given system is detectable. Furthermore, a procedure is given for the construction of the observer. Our approach is based on the properties of real and polynomial matrices.</p>
</abstract>

In this paper the explicit necessary and sufficient conditions for the existence of Luenberger reduced order observer are established. In particular, it is proven that for the given linear time-invariant system of order n, having p linearly independent outputs and m inputs, a Luenberger observer of order (n − p) can be constructed if and only if the given system is detectable. Furthermore, a procedure is given for the construction of the observer. Our approach is based on the properties of real and polynomial matrices.

On the existence of Luenberger reduced order observer

Department of Aeronautical Sciences, Division of Automatic Control

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On the existence of Luenberger reduced order observer"}

In this paper the explicit necessary and sufficient conditions for the existence of Luenberger reduced order observer are established. In particular, it is...

On the existence of Luenberger reduced order observer

Published Online: Apr 11, 2024

Page range: 181 - 198

Received: Sep 01, 2023

Accepted: Nov 01, 2023

DOI: https://doi.org/10.2478/candc-2023-0036

Keywords
Luenberger reduced order observer, necessary and sufficient conditions

© 2023 Konstadinos H. Kiritsis, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On the existence of Luenberger reduced order observer

Published Online: Apr 11, 2024

Page range: 181 - 198

Received: Sep 01, 2023

Accepted: Nov 01, 2023

DOI: https://doi.org/10.2478/candc-2023-0036

KeywordsLuenberger reduced order observer, necessary and sufficient conditions

© 2023 Konstadinos H. Kiritsis, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Luenberger reduced order observer, necessary and sufficient conditions