Unified analysis of stability and dissipativity for inertial memristive multidimensional-valued neural networks with time-varying delays via non-reduced order method.

Abstract

This paper investigates the global dissipativity and stability of inertial memristive multidimensional-valued neural networks (IMMVNNs) with time-varying delays. A unified model is developed based on high-order derivatives, multidimensional algebra, and nonsmooth analysis. By introducing the first-order derivative of the state variables into the Lyapunov functional, the second-order neural network is analyzed directly without order reduction. Using inequality techniques, algebraic criteria for global dissipativity and stability are derived, significantly reducing computational complexity and simplifying the verification process. Finally, the theoretical results are validated through three numerical examples.