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Stability and Stabilization Criteria for Sampled-data Control System via Augmented Lyapunov-Krasovskii Functionals

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  • Control Theory and Applications
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Abstract

This paper proposes improved stability and stabilization conditions for sampled-data systems. Some newly augmented Lyapunov-Krasovskii functionals are constructed to derive enhanced conditions. First, a stability criterion for the sampled-data systems is established in terms of linear matrix inequalities (LMIs). Second, a controller design method is introduced in terms of nonlinear matrix inequalities (NLMIs). In order to solve the NLMI problem, cone complementarity linearization algorithm is introduced. Finally, numerical examples are included to show that the results obtained from the proposed method provide less conservative results, which support the superiority of our criteria.

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Authors and Affiliations

  1. School of Electrical Engineering, Chungbuk National University, 1 Chungdae-ro, Cheongju, 28644, Korea

    Chang Ho Lee, Seung Hoon Lee & Oh Min Kwon

  2. Center of Global Converging Humanities, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu, Yongin, 17104, Korea

    Myeong Jin Park

Authors
  1. Chang Ho Lee
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  2. Seung Hoon Lee
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  3. Myeong Jin Park
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  4. Oh Min Kwon
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Corresponding authors

Correspondence to Myeong Jin Park or Oh Min Kwon.

Additional information

Recommended by Associate Editor Sung Jin Yoo under the direction of Editor Duk-Sun Shim. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2016R1D1A1A09917886) and by Human Resources Program in Energy Technology of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea. (No. 20164030201330). The work of Prof. Park was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government (MSIT; Ministry of Science and ICT) (NRF-2017R1C1B5076878).

Chang Ho Lee received the B.S. and M.S. degrees from the School of Electrical Engineering, Chungbuk National University, Cheongju, Korea, in 2016 and 2018, respectively.

Seung Hoon Lee received the B.S. and M.S. degrees from the School of Electrical Engineering, Chungbuk National University, Cheongju, Korea, in 2014 and 2016, respectively. He is currently pursuing the Ph.D. degree and his current research interests include sampled-data control system, reliable control system, and time-delay systems.

Myeong Jin Park received the B.S. and Ph.D. degrees both in Electrical Engineering from Chungbuk National University, Cheongju, Republic of Korea, in 2009 and 2015, respectively. He was a postdoctoral researcher at School of Electrical Engineering in Chungbuk National University. From April 2017, he is an assistant professor in Center for Global Converging Humanities, Kyung Hee University. His current research interests include consensus problem in multi-agent systems and stability analysis for systems with time-delay.

Oh Min Kwon received the B.S. degree in electronic engineering from Kyungbuk National University, Daegu, Republic of Korea, in 1997, and the Ph.D. degree in electrical and electronic engineering from POSTECH, Pohang, Korea, in 2004. He was a Senior Researcher with the Mechatronics Center of Samsung Heavy Industries, Daejeon, Korea, from 2004 to 2006. He is currently a Professor with the School of Electrical Engineering, Chungbuk National University, Cheongju, Korea. His current research interests include time delay systems, cellular neural networks, robust control and filtering, large-scale systems, secure communication through synchronization between two chaotic systems, complex dynamical networks, multiagent systems, and sampled data control. He has presented over 160 international papers in the above areas. Dr. Kwon was a recipient of the One of the Highly Cited Researchers in the field of mathematics, in 2015, 2016, and 2017. He currently serves as an Associate Editor for Neural Networks, International Journal of Control, Automation and Systems, Journal of Institute of Control, Robotics and Systems, and Journal of Applied Mathematics and Informatics.

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Lee, C.H., Lee, S.H., Park, M.J. et al. Stability and Stabilization Criteria for Sampled-data Control System via Augmented Lyapunov-Krasovskii Functionals. Int. J. Control Autom. Syst. 16, 2290–2302 (2018). https://doi.org/10.1007/s12555-017-0720-z

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  • DOI: https://doi.org/10.1007/s12555-017-0720-z

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