Relaxed Stability Criteria for Delayed Memristor-Based Neural Network Systems via a Novel Matrix-Separation Legendre...

Area of Science:

• Artificial Intelligence
• Control Theory
• Materials Science

Background:

• Memristor-based neural networks (MNNs) offer advanced computing capabilities.
• Time-varying delays in MNNs pose significant challenges to system stability.
• Existing stability analysis methods often exhibit conservatism.

Purpose of the Study:

• To develop novel analytical techniques for stability assessment in MNNs with time-varying delays.
• To reduce the conservatism of stability conditions for MNNs.
• To provide practical and implementable criteria for MNN stability.

Main Methods:

• Proposed a novel matrix-separation Legendre inequality for bounding integral terms.
• Introduced delay-dependent matrices to handle reciprocal terms.
• Developed a new Lyapunov-Krasovskii functional incorporating augmented integrals and delay products.
• Utilized free-weighting matrices, zero-sum equations, and the S-procedure.

Main Results:

• Achieved a tighter hierarchical bound on augmented-type integral terms.
• Derived implementable inequality conditions for stability analysis.
• The proposed method significantly reduces conservatism in stability conditions.
• Validated through three numerical examples and simulations.

Conclusions:

• The novel approach provides less conservative stability conditions for MNNs with time-varying delays.
• The findings contribute to the reliable design and application of MNNs.
• The proposed methods offer a robust framework for stability analysis in complex dynamical systems.