Quasi‐bipartite synchronisation of multiple inertial signed delayed neural networks under distributed event‐triggered impulsive control strategy

Abstract

Abstract The central concern of this paper is to study leader‐following quasi‐bipartite synchronisation of a multiple inertial signed neural networks with varying time‐delay by utilising distributed event‐triggered impulsive control scheme, where connections between adjacent nodes of the neural networks either positive or negative. The second‐order neural networks, called inertial neural networks, can be transformed into differential equations of first‐order by implementing suitable variable substitution. Under certain hypothesis about the node dynamics, signed graph theory and balanced topology of networks, some conditions are derived in terms of lower‐dimensional linear matrix inequalities (LMIs) to achieve leader‐following quasi‐bipartite synchronisation. In addition, a basic algebraic condition is derived to estimate the theoretical upper bound for the error node. Finally, some numerical simulations are provided to illustrate the correctness of the theoretical results.

Keywords

• Algebra
• Combinatorial mathematics
• Control system analysis and synthesis methods
• Stability in control theory