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Static Output-feedback Controller Synthesis for Positive Systems under ℓ∞ Performance

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Abstract

This paper investigates the ℓ∞-induced output-feedback controller synthesis problem for discrete-time positive systems. For positive linear systems, a necessary and sufficient condition for stability and ℓ∞-induced performance is first put forward using a group of linear inequalities. Then, on the basis of these inequalities, the conditions on which static output-feedback controllers exist are set up, and to solve these conditions, a method of iterative convex optimization is provided. Moreover, a complete solution to the synthesis problem of the controller is proposed based on linear programming for positive systems with single output or input. Finally, two examples are presented to illustrate and verify the effective and applicable methods derived in this paper.

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Authors and Affiliations

  1. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P. R. China

    Xiaoming Chen, Mou Chen, Liqun Wang, Jun Shen & Jiapan Hu

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  1. Xiaoming Chen
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  2. Mou Chen
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  3. Liqun Wang
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  4. Jun Shen
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Correspondence to Jun Shen.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Young Ik Son under the direction of Editor Jessie (Ju H.) Park. This work is partially supported by NSFC 61503184, NSFC 61573184, NSFC 61503037, NSFC 61603180 and the Natural Science Foundation of Jiangsu Province under Grant BK20160810.

Xiaoming Chen received her B.S. degree in Automation from Qufu Normal University in 2008. She obtained an M.S. degree in Control Science and Engineering from Harbin Institute of Technology in 2010, and a Ph.D. degree in Control Engineering from the University of Hong Kong in 2014. She joined Nanjing University of Aeronautics and Astronautics, in 2014, taking a lectureship in College of Automation Engineering. Her research interests include positive systems, fuzzy systems, delay systems, 2-D systems, estimation and filtering, stochastic control and robust control.

Mou Chen received his B.Sc. degree in material science and engineering at Nanjing University of Aeronautics & Astronautics, Nanjing, China, in 1998, and his M.Sc. and Ph.D. degrees in automatic control engineering at Nanjing University of Aeronautics & Astronautics, Nanjing, China, in 2004. From June 2008 to September 2009, he was a research fellow in the Department of Electrical and Computer Engineering, the National University of Singapore. He is currently a professor in the College of Automation Engineering at Nanjing University of Aeronautics & Astronautics, China. His research interests include nonlinear control, artificial intelligence, imagine processing and pattern recognition, and flight control.

Liqun Wang was born in Hunan, China, in 1995. He received his B.S. degree in measurement and control technology and instrument from the Harbin Engineering University, Harbin, China, in 2017. He is currently pursuing an M.S. degree with the Nanjing University of Aeronautics and Astronautics, Nanjing, China. His research interests include filter design, 2-D systems, positive systems and fuzzy systems.

Jun Shen received his B.Sc. and M.Sc. degrees from Southeast University, Nanjing, China, in 2008 and 2011, respectively, and his Ph.D. degree from the Department of Mechanical Engineering, the University of Hong Kong, Hong Kong, in 2015. Since 2016 he is an Associate Professor in the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China. His current research interests include positive systems, monotone systems, fractional order systems, model reduction, and robust control and filtering.

Jiapan Hu was born in Zhejiang, China, in 1996. He received his B.S. degree in Electrical Engineering and Automation from the Ningbo University of Technology, Ningbo, China, in 2018. He is currently pursuing an M.S. degree with the Nanjing University of Aeronautics and Astronautics, Nanjing, China. His research interests include filter design, fault detection, positive systems and switched systems.

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Chen, X., Chen, M., Wang, L. et al. Static Output-feedback Controller Synthesis for Positive Systems under ℓ∞ Performance. Int. J. Control Autom. Syst. 17, 2871–2880 (2019). https://doi.org/10.1007/s12555-018-0581-0

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  • DOI: https://doi.org/10.1007/s12555-018-0581-0

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