Stability of nonlinear feedback systems in a Volterra representation

J. W. Glass, Matthew Franchek

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Presented in this paper is a stability condition for a class of nonlinear feedback systems where the plant dynamics can be represented by a finite series of Volterra kernels. The class of Volterra kernels are limited to p-linear stable operators and may contain pure delays. The stability condition requires that the linear kernel is non-zero and that the closed loop characteristic equation associated with the linearized system is stable. Next, a sufficient condition is developed to upper bound the infinity-norm of an external disturbance signal thereby guaranteeing that the internal and output signals of the closed loop nonlinear system are contained in L. These results are then demonstrated on a design example. A frequency domain controller design procedure is also developed using these results where the trade-off between performance and stability are considered for this class of nonlinear feedback systems.

Original languageEnglish (US)
Pages (from-to)799-819
Number of pages21
JournalInternational Journal of Robust and Nonlinear Control
Issue number10
StatePublished - Jan 1 2000

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Chemical Engineering(all)
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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