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Robust model-reference control for descriptor linear systems subject to parameter uncertainties

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Abstract

Robust model-reference control for descriptor linear systems with structural parameter uncertainties is investigated. A sufficient condition for existing a model-reference zero-error asymptotic tracking controller is given. It is shown that the robust model reference control problem can be decomposed into two subproblems: a robust state feedback stabilization problem for descriptor systems subject to parameter uncertainties and a robust compensation problem. The latter aims to find three coefficient matrices which satisfy four matrix equations and simultaneously minimize the effect of the uncertainties to the tracking error. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, the robust compensation problem is converted into a minimization problem with quadratic cost and linear constraints. A numerical example shows the effect of the proposed approach.

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Authors and Affiliations

  1. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, China

    Guangren Duan & Biao Zhang

  2. Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, China

    Biao Zhang

Authors
  1. Guangren Duan
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  2. Biao Zhang
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Additional information

This work was supported in part by the Chinese Outstanding Youth Science Foundation (No. 69925308) and supported by Program for Changjiang Scholars and Innovative Research Team in University.

Guangren DUAN received his B.S. degree in Applied Mathematics, and both his M.S. and Ph.D. degrees in Control Systems Theory. From 1989 to 1991, he was a post-doctoral researcher at Harbin Institute of Technology, where he became a professor of control systems theory in 1991. He visited the University of Hull, UK, and the University of Sheffield, UK from December 1996 to October 1998, and worked at the Queen’s University of Belfast, UK from October 1998 to October 2002. Since August 2000, he has been elected Specially Employed Professor at Harbin Institute of Technology sponsored by the Cheung Kong Scholars Program of the Chinese government. He is currently the Director of the Center for Control Systems and Guidance Technology at Harbin Institute of Technology. He is the author and co-author of over 400 publications. His main research interests include robust control, eigenstructure assignment, descriptor systems, missile autopilot control and magnetic bearing control. He is a Chartered Engineer in the UK, a Senior Member of IEEE and a Fellow of IEE.

Biao ZHANG received his B.S. degree in Mathematics from Peking University, Beijing, in 1984, and M.S. degree in Applied Mathematics from Harbin Institute of Technology, Harbin, in 1989. He is currently an associate professor in the Department of Mathematics at Harbin Institute of Technology, Harbin. His research interests include robust control, model-reference control and descriptor systems.

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Duan, G., Zhang, B. Robust model-reference control for descriptor linear systems subject to parameter uncertainties. J. Control Theory Appl. 5, 213–220 (2007). https://doi.org/10.1007/s11768-006-6025-z

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  • DOI: https://doi.org/10.1007/s11768-006-6025-z

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