This paper aims to propose a stable fuzzy wavelet neural-based adaptive power system stabilizer (SFWNAPSS) for stabilizing the inter-area oscillations in multi-machine power systems. In the proposed approach, a self-recurrent Wavelet Neural Network (SRWNN) is applied with the aim of constructing a self-recurrent consequent part for each fuzzy rule of a Takagi-Sugeno-Kang (TSK) fuzzy model. All parameters of the consequent parts are updated online based on Direct Adaptive Control Theory (DACT) and employing a back-propagation-based approach. The stabilizer initialization is performed using an approach based on genetic algorithm (GA). A Lyapunov-based adaptive learning rates (LALRs) algorithm is also proposed in order to speed up the stabilization rate, as well as to guarantee the convergence of the proposed stabilizer. Therefore, due to having a stable powerful adaptation law, there is no requirement to use any identification process. Kundur's four-machine two-area benchmark power system and six-machine three-area power system are used with the aim of assessing the effectiveness of the proposed stabilizer. The results are promising and show that the inter-area oscillations are successfully damped by the SFWNAPSS. Furthermore, the superiority of the proposed stabilizer is demonstrated over the IEEE standard multi-band power system stabilizer (MB-PSS), and the conventional PSS. mother wavelet translation parameter in SRWNN dilation parameter in SRWNN weight of the self-feedback loop in SRWNN number of input variables total number of the node in the product layer weight parameter in SRWNN product of the wavelets number of fuzzy rules number of samples in the data set SRWNN output center parameter for the Gaussian function scaling parameter for the Gaussian function linguistic term of the input fuzzy variables membership value of the fuzzy set FWNN output (control signal) input variable of FWNN input vector of SFWNAPSS performance index vector of SRWNN parameters Lyapunov function change of Lyapunov function vector of learning rates plant output desired output error between the desired and plant output scaling factor system sensitivity penalty factor scaled control signal chromosome vector rotor speed deviation desired rotor speed deviation 
Direct adaptive power system stabilizer design using fuzzy wavelet neural network with self-recurrent consequent part