Stability Analysis of Fuzzy Control Systems

  • Ian S. Shaw
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 457)


One of the prime concerns facing the designer of any new control system is related to the stability of the system after the controller is introduced. Since in most cases the controller relies on a negative feedback loop, the possibility of system instability exists whenever the loop gain exceeds unity and the loop phase shift exceeds 180 degrees. Every new design needs to be checked to ensure that instability will not occur and every existing design must contain safeguards that unstable modes will be avoided under all operational conditions. The problem of stability in closed-loop control systems has received a considerable degree of academic interest and there are a number of well-established theories to determine the stability limits of conventional controllers. However, with fuzzy controllers the situation is different. In mathematical terms, a fuzzy logic system is a mapping of an input space R n to an output space R m with the following properties:
  • deterministic (the same input condition always results in the same output condition)

  • time-invariant (the input-output function describing the mapping does not change over time)

  • nonlinear (the output variables are not a linear combination of the input variables).


Fuzzy Control Fuzzy Controller Fuzzy Logic System Loop Gain Fuzzy Control System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Ian S. Shaw
    • 1
  1. 1.Industrial Electronic Technology Research GroupRand Afrikaans UniversityJohannesburgRepublic of South Africa

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