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Quantized control for uncertain singular Markovian jump linear systems with general incomplete transition rates

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  • Control Theory and Applications
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Abstract

Quantization is indeed a natural way to take into consideration in the control design of the complexity constraints for the controller as well as the communication constraints in the information exchange between the controller and the plant. This paper is devoted to investigating quantized state-feedback control problems for a class of continuous-time uncertain singular Markovian jump linear systems (CUSMJLSs) with generally uncertain transition rates (GUTRs) and input quantization. In this case, each transition rate can be completely unknown or only its estimate value is known. First, input quantization is introduced, then by introducing new matrix inequality conditions, sufficient conditions are formulated for quantized state-feedback control of CSMJLUSs with GUTRs and input quantization. Finally, a numerical example is presented to illustrate the effectiveness and efficiency of the proposed results.

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Author information

Authors and Affiliations

  1. College of Automation Engineering, Qingdao University of Technology, 2 Changjiang Road, Huangdao District, Qingdao, 266520, China

    Jing Xie

  2. Department of Mathematics, Harbin Institute of Technology(Weihai), 2 Wenhua West Road, Weihai, 264209, China

    Yong-Gui Kao

  3. College of Automation and Electrical Engineering of Qingdao University, Qingdao University, 308 Ningxia Road, Qingdao, 266071, China

    Cai-Hong Zhang

  4. Department of Mechanical Engineering, Politecnico di Milano, 20156, Milan, Italy

    Hamid Reza Karimi

Authors
  1. Jing Xie
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  2. Yong-Gui Kao
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  3. Cai-Hong Zhang
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  4. Hamid Reza Karimi
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Corresponding author

Correspondence to Yong-Gui Kao.

Additional information

Recommended by Associate Editor Yingmin Jia under the direction of Editor Yoshito Ohta. This work was supported by the National Natural Science Foundations of China (61473097) and the Qingdao Postdoctoral Application Research Project (2015117).

Jing Xie received B.S., M.S. and Ph.D. degrees from Ocean University of China in 2009, 2012 and 2015, respectively. She is a Lecturer at the College of Automation Engineering in Qingdao University of Technology, Qingdao, China. Her research interests include singular Markovian jumping systems, sliding mode control and so on.

Yong-Gui Kao received the B.E. degree from Beijing Jiaotong University in 1996. He received his M.E. and Ph.D. degrees from Ocean University of China, in 2005 and 2008, respectively. He is now an Associate Professor at Department of Mathematics, Harbin Institute of Technology (Weihai). His research interest covers stochastic systems, impulsive systems, singular systems, Markovian jumping systems, artificial intelligence, neural networks, stability theory and sliding mode control.

Cai-Hong Zhang received her B.S. degree from Ludong University, Yantai, China in 2004, her M.S. and Ph.D. degrees from Ocean University of China, in 2007 and 2011, respectively. From September 2009 to September 2010, she was a visiting scholar at University of Minnesota Duluth, USA. She is a Lecturer at the College of Automation and Electrical Engineering of Qingdao University, Qingdao, China. Her research interests include nonlinear control and model theory.

Hamid Reza Karimi received the B.Sc. (First Hons.) degree in power systems from the Sharif University of Technology, Tehran, Iran, in 1998, and the M.Sc. and Ph.D. (First Hons.) degrees in control systems engineering from the University of Tehran, Tehran, in 2001 and 2005, respectively. He is currently a professor of Applied Mechanics with the Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy. His current research interests include control systems and mechatronics. He is currently the Editor-in-Chief of the DESIGNS (MDPI Switzerland) and an Editorial Board Member for some international journals, such as the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, the IEEE TRANSACTIONS ON CIRCUIT AND SYSTEMS I: REGULAR PAPERS, the IEEE/ASME TRANSACTIONS ON MECHATRONICS, IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS: SYSTEMS, Information Sciences, the IEEE ACCESS, IFAC-Mechatronics, Neurocomputing, the Asian Journal of Control, the Journal of The Franklin Institute, the International Journal of Control, Automation, and Systems, the International Journal of Fuzzy Systems, the International Journal of e-Navigation and Maritime Economy, and the Journal of Systems and Control Engineering. He is also a member of the IEEE Technical Committee on Systems with Uncertainty, the Committee on Industrial Cyber-Physical Systems, the IFAC Technical Committee on Mechatronic Systems, the Committee on Robust Control, and the Committee on Automotive Control. He is a Senior Member of IEEE and awarded as the 2016 Web of Science Highly Cited Researcher in Engineering.

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Xie, J., Kao, YG., Zhang, CH. et al. Quantized control for uncertain singular Markovian jump linear systems with general incomplete transition rates. Int. J. Control Autom. Syst. 15, 1107–1116 (2017). https://doi.org/10.1007/s12555-014-0171-8

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  • DOI: https://doi.org/10.1007/s12555-014-0171-8

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