Robust Control of Uncertain Systems in Generalized Frequency Domain

In this project, we explore D-decomposition methods applied to control systems with uncertainties. We use a previously developed theory for Generalized Bode Envelopes to find a family of controllers which stabilizes an uncertain system. The approach is similar to classical D-decomposition methods and has been proven to be very useful in the design in the frequency domain. As part of this project, we apply the developed techniques to real-world control systems.

  1. A. Nakhmani, E. Zeheb, M. Lichtsinder, “Robust Controller Design Based on Generalized Bode Envelopes,” IMA Journal of Mathematical Control and Information, DOI:10.1093/imamci/dnr033, Volume 29, Issue 2, pp. 171-198, December 2011.
  2. A. Nakhmani, M. Lichtsinder, E. Zeheb, “Generalized Bode Envelopes and Generalized Nyquist Theorem for Analysis of Uncertain Systems,” International Journal of Robust and Nonlinear Control, Volume 21, Issue 7, pp. 752–767, May 2011.
  3. A. Nakhmani, M. Lichtsinder, E. Zeheb, “Generalized Nyquist Criterion and Generalized Bode Diagram for Analysis and Synthesis of Uncertain Control Systems,” 24th IEEE Convention of Electrical and Electronics Engineers in Israel, pp. 250-254, November 2006.

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Arie Nakhmani is an associate professor of Electrical and Computer Engineering at the University of Alabama at Birmingham (UAB). He joined UAB in 2013. Prior to that, he completed his postdoctoral training at Georgia Tech and Boston University. He is an Associate Scientist in the Comprehensive Cancer Center and director of the ANRY lab at UAB. He is the author of over 120 peer-reviewed research publications and book chapters on robust control, machine learning, signal and image analysis. He is also an author of "Modern Control: State-Space Analysis and Design Methods" textbook published by McGraw Hill in 2020.

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