Stability Analysis of Quaternion-valued Neural Networks with Leakage Delay and Additive Time-varying Delays

TL;DR

This paper develops new stability criteria for quaternion-valued neural networks with leakage and additive delays using Lyapunov-Krasovskii functionals, providing practical conditions in matrix inequality forms.

Contribution

It introduces novel stability analysis methods for QVNNs with complex delay structures, utilizing reciprocal convexity and inequality techniques.

Findings

Derived sufficient stability criteria in QVLMIs and CVLMIs.

Validated criteria through an illustrative example.

Criteria can be efficiently checked using MATLAB toolbox.

Abstract

In this paper, the stability analysis of quaternion-valued neural networks (QVNNs) with both leakage delay and additive time-varying delays is proposed. By employing the Lyapunov-Krasovskii functional method and fully considering the relationship between time-varying delays and upper bounds of delays, some sufficient criteria are derived based on reciprocally convex method and several inequality techniques. The stability criteria are established in two forms: quaternion-valued linear matrix inequalities (QVLMIs) and complex-valued linear matrix inequalities (CVLMIs), in which CVLMIs can be directly resolved by the Yalmip toolbox in MATLAB. Finally, an illustrative example is presented to demonstrate the validity of the theoretical results.