Generalization of stability criterion for Takagi-Sugeno continuous fuzzy model (Q698836)

New stability conditions are presented to study the stability of the Takagi-Sugeno model. The main characteristic of the proposed stability method is the presentation of an alternative way of checking the stability of fuzzy systems, as shown through the derived stability conditions. Another advantage is that the authors first derive a general stability condition that requires the search for the \(P\) matrix. Then this condition is modified so that it does not need the calculation of this matrix, which reduces significantly the difficulties of applying it and gives faster computations. The stability analysis of a fuzzy system, which is achieved by blending these linear models, is studied. The conditions derived can be applied not only to fuzzy systems but also to other nonlinear ones. The new stability conditions can be regarded as a general solution for a Takagi-Sugeno system in which the offset term is not equal to zero. Finally, the suggested stability theorems are verified by some illustrative examples.