A Switched System Model for Exponential Stability and Dissipativity of Delayed Neural Networks

Area of Science:

• Control Systems Engineering
• Computational Neuroscience
• Applied Mathematics

Background:

• Neural networks with time-varying delays present significant stability challenges.
• Existing methods for analyzing these systems often lack sufficient information regarding delay dynamics.
• Lyapunov-Krasovskii functionals (LKFs) are crucial for stability analysis but require careful construction for time-varying delays.

Purpose of the Study:

• To develop novel criteria for ensuring exponential stability and dissipativity in delayed neural networks (DNNs) with time-varying delays.
• To improve the analysis of DNNs by incorporating more information about the delay and its derivative.
• To provide a more flexible framework for constructing LKFs.

Main Methods:

• Modeling the delayed neural network (DNN) as a switching system with two modes based on the sign of the delay derivative.
• Utilizing the average dwell time (ADT) technique to analyze the switching system.
• Developing new criteria for exponential stability and exponential dissipativity based on the constructed LKFs.

Main Results:

• Several new criteria for exponential stability and exponential dissipativity of DNNs with time-varying delays were derived.
• The proposed switching system model offers greater flexibility in LKF construction, allowing for different Lyapunov matrices per mode.
• The derived criteria demonstrate superiority over existing methods in benchmark examples and a practical control system.

Conclusions:

• The proposed switching system approach and ADT technique effectively address the challenges of time-varying delays in DNN stability analysis.
• The new criteria provide a robust and practical method for ensuring exponential stability and dissipativity.
• The findings have implications for the reliable design and control of complex neural network systems.