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Robust observer-based control for uncertain discrete-time piecewise affine systems

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Abstract

The main contribution of this paper is to present a novel robust observer-based controller design method for discrete-time piecewise affine systems with norm-bounded uncertainties. The key ideas are to construct a piecewise-quadratic Lyapunov function to guarantee the stability of the closed-loop systems, approximate polytopic operating regions by ellipsoids, and use the singular value decomposition technique to treat the constraint of matrix equality. It is shown that the suggested control method can be formulated as linear matrix inequalities that are numerically feasible with commercially available software. A numerical example is also given to verify the proposed approach.

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Authors and Affiliations

  1. AVIC (Aviation Industry Corporation of China) China Aviation Motor Control System Institute, Wuxi Jiangsu, 214063, China

    Yahui Gao

  2. Department of Control Science and Engineering, Harbin Institute of Technology, Harbin Heilongjiang, 150001, China

    Zhiyuan Liu

  3. Department of Control Science and Engineering, Jilin University, Changchun Jilin, 130025, China

    Hong Chen

Authors
  1. Yahui Gao
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  2. Zhiyuan Liu
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  3. Hong Chen
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Corresponding author

Correspondence to Yahui Gao.

Additional information

Yahui GAO was born in 1981. He received his B.S., M.S. and Ph.D. degrees from Harbin Institute of Technology in 2003, 2005 and 2010, respectively. Currently, he works in AVIC China Aviation Motor Control System Institute. His research interests include aero-engine control, hybrid system control, robust control, and model predictive control.

Zhiyuan LIU was born in 1957. He received his Ph.D. degree from Harbin Institute of Technology in 1992. Currently, he is a professor at Harbin Institute of Technology. His research interests include automotive electronic control, robotics, robust control, and model predictive control.

Hong CHEN was born in 1963. She received her B.S. and M.S. degrees in Process Control from Zhejiang University in 1983 and 1986, respectively, and Ph.D. degree from University of Stuttgart, Germany in 1997. In 1986, she joined Jilin University of Technology. From 1993 to 1997, she was a ‘Wissenschaftlicher Mitarbeiter’ at Institut fuer Systemdynamik und Regelungstechnik, University of Stuttgart. Since 1999, she has been a professor at Jilin University. Her research interests include model predictive control, optimal and robust control, and applications in process engineering and mechatronic systems.

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Gao, Y., Liu, Z. & Chen, H. Robust observer-based control for uncertain discrete-time piecewise affine systems. J. Control Theory Appl. 10, 236–243 (2012). https://doi.org/10.1007/s11768-012-9145-7

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  • DOI: https://doi.org/10.1007/s11768-012-9145-7

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