Stable Fuzzy Control System by Design - Fuzzy Modeling and Control: Theory and Applications - page 86

In these figures it can be seen that indeed, all paths that do not leave the universe
of discourse of the state variables tend to equilibrium at the origin. The stability of
those trajectories that leave the universe of discourse of the state variables, shown
in dotted line can not be guaranteed, since the fuzzy model of the plant need not be
valid outside the range of values for which it was obtained. Therefore, through the
failure to ensure compliance of Theorem 4.1 for such paths can not formally ensure
stability.
4.5 Conclusions
This chapter has shown a completely general formal methodology that allows the
synthesis of stable fuzzy controllers systems by design, that is, where the stability of
the closed loop system is ensured during the design process of the fuzzy controller
itself. It is also proposed an algorithm to design a controller that ensures the stability
of the closed loop fuzzy control system, and have been presented several examples.
Acknowledgments The authors would like to thank the Spanish Ministry of Economy and
Competitiveness for its support to this work through projects DPI2010-17123 and DPI2010-21247-
C02-01, the Regional Government of Andalusia (Spain) for supporting TEP-6124 project, as well
as the European Union Regional Development for funding the last two projects.
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