Lyapunov functions and global frequency domain stability criteria for a class of stochastic feedback systems

  • Jacques L. Willems
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 294)


This paper deals with the stability of a particular class of stochastic systems; feedback systems are considered which have a feedback gain with a deterministic gain which may be nonlinear and/or time-varying and a stochastic component which is white noise. Lyapunov functions are constructed and criteria for global stability are derived similar to the results available for related deterministic feedback systems, such as the Routh-Hurwitz criterion, the Popov criterion, and the circle criteria.


Lyapunov Function Feedback Gain Null Solution Quadratic Lyapunov Function Circle Criterion 
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Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Jacques L. Willems
    • 1
  1. 1.University of GentGentBelgium

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