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LMI-based robust sampled-data stabilization of polytopic LTI systems: A truncated power series expansion approach

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  • Control Theory
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Abstract

For continuous-time linear time-invariant (LTI) systems with polytopic uncertainties, we develop a robust sampled-data state-feedback control design scheme in terms of linear matrix inequalities (LMIs). Truncated power series expansions are used to approximate a discretized model of the original continuous-time system. The system matrices obtained by using the power series approximations are then expressed as homogeneous polynomial parameter-dependent (HPPD) matrices of finite degrees, and conditions for designing the controller are formulated as a HPPD matrix inequality, which can be solved by means of a recent LMI relaxation technique to test the positivity of HPPD matrices with variables in the simplex. To take care of the errors induced by the remainder terms of the truncated power series, the terms are considered as norm bounded uncertainties and then incorporated into the proposed LMI conditions. Finally, examples are used to illustrate the approach.

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, 47906, USA

    Dong Hwan Lee

  2. Department of Control and Robotics Engineering, Kunsan National University, Kunsan, Chonbuk, 573-701, Korea

    Young Hoon Joo

Authors
  1. Dong Hwan Lee
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Correspondence to Young Hoon Joo.

Additional information

Dong Hwan Lee received his B.S. degree in Electronic Engineering from Konkuk University, Seoul, Korea, in 2008 and his M.S. degree in Electrical and Electronic Engineering, Yonsei University, Seoul, Korea, in 2010. From 2014, he is working toward a Ph.D. degree in the Department of Electrical and Computer Engineering, Purdue University, USA. His current research interests include stability analysis in fuzzy systems, fuzzy-model-based control, and robust control of uncertain linear systems.

Young Hoon Joo received his B.S., M.S., and Ph.D. degrees in Electrical Engineering from Yonsei University, Seoul, Korea, in 1982, 1984, and 1995, respectively. He worked with Samsung Electronics Company, Seoul, Korea, from 1986 to 1995, as a project manager. He was with the University of Houston, Houston, TX, from 1998 to 1999, as a visiting professor in the Department of Electrical and Computer Engineering. He is currently a professor in the Department of Control and Robotics Engineering, Kunsan National University, Korea. His major interest is mainly in the field of intelligent robot, robot vision, intelligent control, human-robot interaction, wind-farm control, and intelligent surveillance systems. He served as President for Korea Institute of Intelligent Systems (KIIS) (2008–2009) and the Vice-President for the Korean Institute of Electrical Engineers (KIEE) (2013–2014); and is serving as Editor-in-Chief for the International Journal of Control, Automation, and Systems (IJCAS) (2014-present).

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Lee, D.H., Joo, Y.H. LMI-based robust sampled-data stabilization of polytopic LTI systems: A truncated power series expansion approach. Int. J. Control Autom. Syst. 13, 284–291 (2015). https://doi.org/10.1007/s12555-014-0328-5

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  • DOI: https://doi.org/10.1007/s12555-014-0328-5

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