<i>H</i> _∞ Pinning Synchronization Control for Markovian Intermittent Time-Varying Coupled Neural Networks Under Multiplicative Noises

Abstract

In this paper, we study <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty} $ </tex-math></inline-formula> pinning synchronization control problem for Markovian intermittent coupled neural networks with time-varying coupling strengths, and the influence of multiplicative noises on actuators is also considered. A set of random variables of known mathematic expectations and variances is introduced to describe stochastically changing interactions among neural networks, and a two-states Markov chain is used to characterize the intermittently time-varying interactive relationship between neural network and its neighboring neural networks. By analyzing stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty} $ </tex-math></inline-formula> disturbance attenuation performance of the obtained synchronization error systems, two sufficient conditions are derived to ensure global synchronization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty} $ </tex-math></inline-formula> global synchronization of the controlled networks respectively. Then, the pinning synchronization controllers are designed, and we can change control cost by varying the number of pinned nodes. Finally, an algorithm resulting the set of optimal pinned nodes which minimizes the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty} $ </tex-math></inline-formula> disturbance attenuation performance index is provided, and a numerical example illustrating the effectiveness of the obtained theoretical results is given.