Research on extended dissipativity for discrete-time inertial neural networks

This paper presents the first investigation into the extended dissipativity, a unified performance index, for discrete-time inertial neural networks (DINNs). Different from recent related works that concentrate primarily on delay information, this paper is built upon the joint consideration of delays and neuron activation functions to construct a novel Lyapunov–Krasovskii functional (LKF). A key innovation in the LKF is the introduction of the delay-dependent Luire–Postnikov-type (DLPT) integral terms of the neuron activation functions that capture sector restrictions of activation functions. Then, by the extended reciprocally convex matrix inequality (ERCMI) and a slope restriction integral inequality, not only the less-conservative extended dissipativity criterion but also the stability criterion for DINNs are derived. The advantages of the criteria are confirmed via two numerical examples.