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Nonlinear Robust H∞ Control With State-Dependent Scaling

[+] Author Affiliations
Scott Hays, Fen Wu

North Carolina State University, Raleigh, NC

Paper No. DSCC2011-5994, pp. 581-588; 8 pages
  • ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control
  • ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 1
  • Arlington, Virginia, USA, October 31–November 2, 2011
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-5475-4
  • Copyright © 2011 by ASME


This paper addresses the design of nonlinear robust H ∞ controllers for nonlinear uncertain systems with polynomial vector field and norm bounded uncertainties. We derive state-dependent matrix inequalities, using Lyapunov’s direct method, that stabilize the nonlinear systems and guarantee robust performance using nonlinear state-feedback control. The state-dependent synthesis conditions incorporate state-dependent scaling to minimize the ℒ2 gain of the disturbance/output. Sum-of-squares (SOS) optimization is applied to solve the resulting synthesis condition with optimized ℒ2 gain for the nonlinear system, without requiring an iterative approach. Finally, a design example of nonlinear Van der Pol equation is presented.

Copyright © 2011 by ASME



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