Stability analysis of fractional-order neural networks with time-varying delay utilizing free-matrix-based integral inequalities

The stability problem of fractional-order neural networks in consideration of time-varying delay is addressed by utilizing Lyapunov functional approach in this paper. Firstly, a class of novel Lyapunov-Krasovskii functions are designed to deal with the time-varying delay terms, which reduces the conservatism of the stability criteria. In addition, to estimate the fractional-order derivative of the Lyapunov-Krasovskii functions, a novel free-matrix-based fractional-order integral inequality is then established, which encompasses the Wirtinger one and leads to tractable linear matrix inequality criteria. Then, based on the designed adaptive control and the proposed Lyapunov-Krasovskii functions, some stability criteria depending on time-varying delay information and fractional-order α are deduced. Finally, numerical simulation shows that the presented approach can significantly reduce the conservatism of the existing results and has a broader application prospect.