Finite-Time $\mathcal {L}_{2}$-$\mathcal {L}_{\infty }$ Synchronization for Semi-Markov Jump Inertial Neural Networks Using Sampled Data
Jing Wang, Tingting Ru, Hao Shen, Jinde Cao, Ju H. Park
Abstract
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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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.