Results on passivity analysis of delayed fractional-order neural networks subject to periodic impulses via refined integral inequalities

This manuscript is concerned with analysing the passiveness of fractional-order neural networks with parameter uncertainties, delays, and periodic impulses. This work mainly focuses on the issue of the lack of suitable Lyapunov functionals for delay-dependent stability/passivity analysis of fractional-order systems (FOSs). First, a fractional-order free-matrix-based integral inequality is derived to estimate the fractional derivative of constructed Lyapunov function. Second, by introducing a fractional parameter, a refined looped functional is structured so that the resulting linear matrix inequality (LMI) includes all the information of delays in states, inter-impulse time, and impulse gain matrix. Then by fractional-order Lyapunov direct method, certain new delay-dependent passivity and stability criteria for the considered FONNs with and without delays are established in the form of LMIs. Numerical examples with simulations are given to pledge the correctness of the proposed theoretical results. Finally, a practical application of developed results is given.