Finite-Time $\mathcal{L}_{2}$-$\mathcal{L}_{\infty}$ Synchronization for semi-Markov Jump Inertial Neural Networks Using Sampled Data

This paper investigates the finite-time synchronization issue for semi-Markov jump inertial neural networks, in which the sampled-data control is employed to alleviate the burden of the limited communication bandwidth. Due to the existence of inertial item, the semi-Markov jump inertial neural networks as hybrid neural systems, are depicted with second-order derivatives for the first time, which can be turned to first-order derivatives by the variable transformation. Furthermore, by applying appropriate integral inequalities and constructing the proper Lyapunov functional, some sufficient conditions, which not only guarantee the finite-time synchronization of the resulting error system but also ensure a specified level of $\mathcal {L}_{2}$ - $\mathcal {L}_{\infty }$ performance, are acquired based on the optimization of integral inequality technique. A numerical example is, eventually, proposed to substantiate the validity of the developed method.