On fixed-time interlayer synchronization of two-layer multiweighted complex dynamic networks: An economic and practical non-chattering adaptive control approach

This paper investigates the adaptive fixed-time (FxT) interlayer synchronization issue of two-layer complex dynamic networks (CDNs), where both multiple weights and interlayer links are considered. Above all, a new FxT stability lemma is given, which offers a more flexible condition and some more precise estimates of stabilized convergence time compared with the existing results. Subsequently, an economic and practical non-chattering continuous adaptive controller is designed, which is superior to the currently available ones by excluding the signum function and linear part and removing the parity restriction on the exponents in control law. Furthermore, by means of the Lyapunov method and the newly-established FxT stability theory, some novel FxT interlayer synchronization criteria are derived for the addressed two-layer multiweighted CDNs with the designed non-chattering continuous adaptive controller, and the synchronized settling time (SST) is also reckoned. It is found that the interlayer links weights can contribute to the interlayer synchronization, and the SST becomes smaller with the increase of interlayer link weight. Finally, the proposed results are validated by numerical examples.