Mean-squared exponential stabilization of Takagi-Sugeno fuzzy genetic oscillator networks involving switching control failures: A frame of spatio-temporal discretizations

This article considers global asymptotic and exponential stabilizations in the mean-square sense of space-time discrete Takagi-Sugeno (T-S) fuzzy genetic oscillator networks (GONs) with switching actuator failures and Dirichlet controlled boundaries. It presents some exciting results for the criteria of global asymptotic stabilization in the mean-square sense for the proposed discrete T-S fuzzy GONs via the approaches of the Lyapunov-Krasovskii function, the discrete Wirtinger inequality, and the discrete formula of integration by parts. Besides, our research delves into the exciting possibility of global exponential stabilization in the mean-square sense, which offers a more comprehensive view of stabilized T-S fuzzy GONs than asymptotic stabilization. More critically, this study shows that global mean-square stabilizations of space-time discrete T-S fuzzy GONs can be achieved better by taking the values with the smaller diffusion intensities, smaller coupling strengths and bigger connection weights. Compared to the previous literatures, this paper offers a framework to discuss the issues of global stabilizations for space-time discrete T-S fuzzy GONs with switching actuator failures through the boundary controls, and the results are applicable in a wide range of applications. And finally, an illustrative example is presented to prove the method's validity.