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H ∞ control of singular systems via delta operator method

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  • Control Theory
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Abstract

This paper studies the problem of state feedback H ∞ control for singular systems through delta operator approach. A necessary and sufficient condition is presented such that a singular delta operator system is admissible with a prescribed H ∞ performance, which can provide a unified framework of the existing H ∞ performance analysis results for both continuous case and discrete case. The existence condition and explicit expression of a desirable H ∞ controller are also obtained for singular delta operator systems. The proposed design method can be used for both singular continuous systems and singular discrete systems directly. The corresponding design procedures, which simplify the classical approaches, are discussed and presented. All obtained conditions in this paper are in the form of strict linear matrix inequalities whose feasible solutions can be found by standard linear programming method. Numerical examples are provided to illustrate the effectiveness of the theoretical results obtained in this paper.

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Authors and Affiliations

  1. College of Automation Engineering, Qingdao University, Qingdao Shandong, 266071, China

    Xin-zhuang Dong

  2. Department of Mathematics, Southern Illinois University, Carbondale IL, 62901, U.S.A.

    Mingqing Xiao

Authors
  1. Xin-zhuang Dong
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  2. Mingqing Xiao
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Corresponding author

Correspondence to Xin-zhuang Dong.

Additional information

Xin-zhuang Dong received her B.Sc. degree in Applied Mathematics from the Institute of Information Engineering of People’s Liberation Army (PLA), China, in 1994, an M.Sc. degree from the Institute of Electronic Technology of PLA, China, in 1998, and a Ph.D. degree in Control Theory and Control Engineering from Northeastern University, China, in 2004, respectively. From September 2004 to August 2006, she was a Postdoctoral Researcher in the Academy of Mathematics and Systems Science, Chinese Academy of Science. From September 2013 to April 2014, she was a Visiting Scholar in Southern Illinois University. Since August 2006, she has been affiliated with College of Automation Engineering, Qingdao University. She is an Associate Professor at the Department of Control Engineering. Her research interests include singular system theory, robust control, sliding mode control, and delta operator systems.

Mingqing Xiao received his Ph.D. degree from the University of Illinois at Urbana-Champaign, USA in 1997. He is currently a professor at the Department of Mathematics, Southern Illinois University at Carbondale. His research interests include dynamical system theory, nonlinear observer design, and control of distributed parameter systems.

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Dong, Xz., Xiao, M. H ∞ control of singular systems via delta operator method. Int. J. Control Autom. Syst. 13, 643–651 (2015). https://doi.org/10.1007/s12555-013-0111-z

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  • DOI: https://doi.org/10.1007/s12555-013-0111-z

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