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Reduced-order Observers Design for Unknown Inputs Switched Systems without Strongly Detectable of Subsystems

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  • Control Theory and Applications
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Abstract

This paper investigates the reduced-order switched observers for switched linear systems with unknown inputs when none subsystems are strongly detectable under dwell time switching. A time-varying disturbance-decoupling state coordinate transformation is first utilized to decouples the unknown input from a subset of the transformed state coordinates. Secondly, a linear coordinate transformation is constructed to decompose the system state into directly available state component parts and non-direct available state component parts. The existence conditions of the reduced-order switched observers are derived by both restricting the upper bounds and the lower bounds of dwell time, decreasing the energy of switched systems at switching times, and confining the growth of subsystems’ Lyapunov functions, and the reduced-order switched observers are constructed. Stability analysis of switched error dynamics is also presented. Then, the proposed reduced-order switched observers asymptotically converges to the state under the designed dwell time switching signal. Finally, an example confirms the effectiveness of the proposed method.

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Funding

This work was partially supported by National Natural Science Foundation of China (62073157), Scientific Research Fund of Educational Department of Liaoning Province (LZD201901), and Liaoning Revitalization Talents Program (XLYC1807012).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Liaoning University, Shenyang, 110036, China

    Ruicheng Ma, Haozhe Pang, Lulu Fu & Yetian Fan

Authors
  1. Ruicheng Ma
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  2. Haozhe Pang
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  3. Lulu Fu
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  4. Yetian Fan
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Corresponding author

Correspondence to Yetian Fan.

Additional information

Ruicheng Ma received his M.S. degree in applied mathematics from Liaoning University, China, in 2008. He completed his Ph.D. in control theory and control engineering from Northeastern University, China, in 2012. He is currently a professor with the School of Mathematics and Statistics, Liaoning University, China. His research interests include switched systems, hybrid control, and nonlinear systems.

Haozhe Pang received her B.S. degree in mathematics and applied mathematics in 2018 from Shihezi University, China. Now she is currently pursuing an M.S. degree at School of Mathematics and Statistics, Liaoning University, Shenyang, China. Her research interests include switched systems, nonlinear systems, and observers design.

Lulu Fu received her B.S. degree in Information and Computing Science from Liaoning University of Technology, Jinzhou, China, in 2019. She is now working towards an M.S. degree in Operations Research and Cybernetics from Liaoning University, Shenyang, China. Her current research interests include switched systems, nonlinear systems, and optimal control.

Yetian Fan received his B.S. and Ph.D. degrees in the School of Mathematical Science from Dalian University of Technology, Dalian, China, in 2010 and 2017, respectively. Currently, he is a lecturer in the School of Mathematics and Statistics, Liaoning University, China. His research interests include switched systems, machine learning, and bioinformatics.

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Ma, R., Pang, H., Fu, L. et al. Reduced-order Observers Design for Unknown Inputs Switched Systems without Strongly Detectable of Subsystems. Int. J. Control Autom. Syst. 20, 1275–1282 (2022). https://doi.org/10.1007/s12555-021-0168-z

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  • DOI: https://doi.org/10.1007/s12555-021-0168-z

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