Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(4): 1105-1115

https://doi.org/10.1007/s12555-023-0103-6

© The International Journal of Control, Automation, and Systems

Interval Reduced-order Switched Positive Observers for Uncertain Switched Positive Linear Systems

Naohisa Otsuka*, Daiki Kakehi, and Przemysław Ignaciuk

Tokyo Denki University

Abstract

In this paper, existence conditions and a design procedure of reduced-order switched positive observers for continuous- and discrete-time switched positive linear systems with uncertainty are established. In the analyzed class, arbitrary switching is permitted, whereas the uncertainty expressed via matrix inequalities concerns both the initial state and system parameters. Positive lower and positive upper interval switched observers are obtained. The proposed observers are of (n− p) order, where n is the dimension of the state vector and p is the rank of the output matrix, i.e., p-dimensional measurement information. Moreover, as a special case, existence conditions and a design procedure of reduced-order positive observers for uncertain positive linear systems without switching are provided. The theoretical findings are illustrated by two numerical examples for continuous- and discrete-time systems.

Keywords Interval switched positive observer, reduced-order switched observer, uncertain switched positive linear systems.

Article

Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(4): 1105-1115

Published online April 1, 2024 https://doi.org/10.1007/s12555-023-0103-6

Copyright © The International Journal of Control, Automation, and Systems.

Interval Reduced-order Switched Positive Observers for Uncertain Switched Positive Linear Systems

Naohisa Otsuka*, Daiki Kakehi, and Przemysław Ignaciuk

Tokyo Denki University

Abstract

In this paper, existence conditions and a design procedure of reduced-order switched positive observers for continuous- and discrete-time switched positive linear systems with uncertainty are established. In the analyzed class, arbitrary switching is permitted, whereas the uncertainty expressed via matrix inequalities concerns both the initial state and system parameters. Positive lower and positive upper interval switched observers are obtained. The proposed observers are of (n− p) order, where n is the dimension of the state vector and p is the rank of the output matrix, i.e., p-dimensional measurement information. Moreover, as a special case, existence conditions and a design procedure of reduced-order positive observers for uncertain positive linear systems without switching are provided. The theoretical findings are illustrated by two numerical examples for continuous- and discrete-time systems.

Keywords: Interval switched positive observer, reduced-order switched observer, uncertain switched positive linear systems.

IJCAS
April 2024

Vol. 22, No. 4, pp. 1105~1460

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