Non-fragile robust finite-time stabilization and \(H_{\infty }\) performance analysis for fractional-order delayed neural networks with discontinuous activations under the asynchronous switching

In this paper, the global non-fragile robust finite-time stabilization and \(H_{\infty }\) performance analysis are investigated for uncertain switched fractional-order neural networks with discontinuous activations, time delay and external disturbance under the asynchronous switching. Firstly, a new inequality, which is concerned with the fractional derivative of the variable upper limit integral for the nonsmooth integrable functional, is developed. Secondly, the non-fragile switched controller with two types of gain perturbations is designed. Under the Filippov fractional differential inclusion framework, the global non-fragile robust finite-time stabilization conditions are addressed in terms of linear matrix inequalities (LMIs) by applying nonsmooth analysis theory, inequality analysis technique, average dwell-time method and Lyapunov functional approach. In addition, the global non-fragile robust finite-time \(H_{\infty }\) performance analysis is performed, and the global non-fragile robust finite-time stabilization conditions with \(H_{\infty }\) disturbance attenuation level are also derived in the form of LMIs. Finally, two numerical examples are given to illustrate the feasibility of the proposed non-fragile switched controller and the validity of the theoretical results.