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

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  • Control Theory and Applications
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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.

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Authors and Affiliations

  1. Division of Science, the School of Schience and Engineering, Tokyo Denki University, Hatoyama-Machi, Hiki-Gun, Saitama, 350-0394, Japan

    Naohisa Otsuka

  2. Graduate School of Science and Engineering, Tokyo Denki University, Hatoyama-Machi, Hiki-Gun, Saitama, 350-0394, Japan

    Daiki Kakehi

  3. Institute of Information Technology, Lodz University of Technology, al. Politechniki 8, 93-590, Łódź, Poland

    Przemysław Ignaciuk

Authors
  1. Naohisa Otsuka
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  2. Daiki Kakehi
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Correspondence to Naohisa Otsuka.

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The authors would like to express their gratitude to the Senior Editor, Associate Editor, and Reviewers for many helpful and valuable comments and suggestions. The work of N. Otsuka was supported in part by JSPS KAKENHI Grant Number 19K04443. The work of P. Ignaciuk was supported by a project “Robust control solutions for multi-channel networked flows” no. 2021/41/B/ST7/00108 financed by the National Science Centre, Poland.

Naohisa Otsuka received his B.S. and M.S. degrees in mathematical sciences, from Tokyo Denki University (TDU), in 1984 and 1986, respectively. In 1992, he received a doctor of science in mathematical sciences from the Graduate School of Science and Engineering of TDU. From 1986 to 1992, he served as a Research Associate in the Department of Information Sciences, TDU. In April 1992, he moved to the Institute of Information Sciences and Electronics, University of Tsukuba as a Research Associate and served as an Assistant Professor of the same University from 1993 to September 2000. From October 2000 to September 2003 he served as an Associate Professor in the Department of Information Sciences, TDU. From October 2003 to 2007, he served as a Professor in the same department. Since April 2007, he has been with the Division of Science in TDU as a Professor. His research interests include geometric control theory, switched systems, epidemic mathematical models, robust control, and infinite-dimensional linear systems. He served as an associate editor of Journal of The Franklin Institute from 2005 to 2016. Dr. Otsuka is an editor of Mathematical Problems in Engineering and is a member of IFAC Technical Committee on Linear Control Systems. He is a member of the Society of Instrument and Control Engineers of Japan (SICE), IEEE and SIAM.

Daiki Kakehi received his B.S. degree in science and engineering and an M.S. degree from the Graduate School of Science and Engineering, from Tokyo Denki University (TDU), in 2017 and 2019, respectively. He is currently working for a company in Japan. His research interests include switched linear systems, positive linear systems, and observer design.

Przemysław Ignacuik received his M.Sc. (with Hons.) degree in telecommunications and computer science and a Ph.D. (with Hons.) degree in control engineering and robotics from Lodz University of Technology, Łódź, Poland, in 2005 and 2008, respectively, and the Habilitation degree in computer science from Systems Research Institute Polish Academy of Sciences, Warsaw, Poland, in 2014. He worked for three years as a full-time Analyst and IT System Designer with the Telecommunications Industry. He then joined the Institute of Automatic Control, and since 2011, he has been with the Institute of Information Technology, Lodz University of Technology, where he is currently an Assistant Professor and the Head of a research group dedicated to complex system analysis and design. He has authored or coauthored one book, 15 monograph chapters, and over 180 journal and conference papers, in the area of control systems, communication and logistic networks. His research interests include networked control systems, robust control, dynamical optimization, and time-delay systems.

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Otsuka, N., Kakehi, D. & Ignaciuk, P. Interval Reduced-order Switched Positive Observers for Uncertain Switched Positive Linear Systems. Int. J. Control Autom. Syst. 22, 1105–1115 (2024). https://doi.org/10.1007/s12555-023-0103-6

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

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