Study of the stability of fuzzy controllers by an estimation of the acctraction regions: a vector norm approach (Q1876943)

The study focuses on the stability of fuzzy controllers realized in the framework of vector norms. The many-input-single-output fuzzy controller under consideration satisfies the following assumptions: (a) input fuzzy sets are described by trapezoidal membership functions, (b) AND aggregation of the conditions is realized via a minimum function, and (c) the output of the controller is formed through a singleton fuzzification. The nonlinear system under control is governed by the expression \(dx/dt = A(t, x,\omega)x + B(t,x,\omega)\) with \(\omega\) representing perturbations of the state. Following the technique of stable overvalueing systems, the stability properties of fuzzy controllers are investigated. Their attractors are formed with the aid of the comparison principle. The robustness aspects of the controllers are presented as well. A series of illustrative examples is included.