LMI-based design of stabilizing fuzzy controllers for nonlinear systems described by Takagi-Sugeno fuzzy model.

*(English)*Zbl 0980.93039The authors address the problem of designing fuzzy controllers with guaranteed stability for nonlinear systems described by the TS (Takagi-Sugeno) fuzzy model. They classify the TS fuzzy systems into three families TS(B), TS(Bi) and TS(aiB) based on how diverse their input matrices are, and present a unique controller synthesis procedure for each family. The procedures provide the TS fuzzy controllers or their modified versions according to which family the given system belongs to. An example of controlling a nonlinear mass-spring-damper system is considered. Since each procedure is essentially based on the LMI (linear matrix inequalities) feasibility problem, the LMI Control Toolbox in the Matlab environment was effectively utilized in solving the problem, and satisfactory simulation results were obtained.

Reviewer: George S.Stavrakakis (Chania)

##### MSC:

93C42 | Fuzzy control/observation systems |

93D15 | Stabilization of systems by feedback |

15A39 | Linear inequalities of matrices |

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\textit{J. Park} et al., Fuzzy Sets Syst. 122, No. 1, 73--82 (2001; Zbl 0980.93039)

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