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A Lyapunov Proof of Stability for Parallel Controllers of SISO Systems

[+] Author Affiliations
Andy Zelenak, Meredith Pitsch, Benito Fernández, Mitch Pryor

University of Texas at Austin, Austin, TX

Paper No. DETC2017-68036, pp. V006T10A017; 8 pages
doi:10.1115/DETC2017-68036
From:
  • ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Cleveland, Ohio, USA, August 6–9, 2017
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5820-2
  • Copyright © 2017 by ASME

abstract

For dynamic systems, it is known that stability (in general) cannot be guaranteed for individually-stabilizing controllers in combination, so the combined system must be analyzed to ensure stability. This paper presents a simple, graphical proof of Lyapunov stability for parallel controllers of SISO, input-affine, autonomous systems. This encompasses a broad range of all linear autonomous systems and many nonlinear, autonomous SISO systems. The proof allows Lyapunov stability theory to be used instead of the more complex and restrictive passivity approach. The paper also explains why it is often desirable to place controllers in parallel.

Copyright © 2017 by ASME

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