Further enhancement of stability and stabilisability margin for Takagi–Sugeno fuzzy systems

The authors consider in this study the problem of reducing conservatism in stability and stabilisation margin of continuous-time Takagi–Sugeno (T–S) fuzzy systems, where the fuzzy weighting functions are assumed to be differentiable and their ranges of variation are assumed to be bounded by some parameters. To compensate for the latter constraint, the conventional quadratic relaxation technique is appropriately modified and the free weighting matrix for the former assumption is further indexed in accordance with the fuzzy weighting functions to derive more degrees of freedom. By applying the relaxed free weighting matrices into the resulting quadratic summation representation and by utilising the linearity of the constraints on the time-derivative of the membership functions, better performance behaviour can be achieved over existing works, which is demonstrated theoretically and by some examples.