Type-Dependent Average Dwell Time Method and Its Application to Delayed Neural Networks With Large Delays

Area of Science:

• Control Theory
• Computational Neuroscience
• Systems Engineering

Background:

• Delayed neural networks are crucial in modeling complex systems.
• Analyzing stability with large delays remains a significant challenge.
• Existing methods often exhibit conservatism.

Purpose of the Study:

• To develop a novel method for guaranteeing the stability of delayed neural networks with large delays.
• To reduce the conservatism in stability criteria for these systems.
• To propose an improved allowable maximum delay bound (AMDB).

Main Methods:

• Decomposing the original large delay into multiple smaller parts.
• Modeling the delayed neural network as a switched system.
• Employing type-dependent average dwell time (ADT) for system switches.
• Utilizing multiple Lyapunov functions (MLFs) for stability analysis.

Main Results:

• A new stability condition for delayed neural networks with large delays is established.
• The proposed type-dependent ADT effectively manages switches between subsystems.
• Incorporating more delayed state vectors increases the AMDB.
• The method demonstrates reduced conservatism compared to existing approaches.

Conclusions:

• The novel approach effectively guarantees global exponential stability for delayed neural networks.
• The proposed method offers superior performance and reduced conservatism.
• Numerical examples validate the effectiveness and superiority of the technique.