Delay-Dependent Stability Analysis for Switched Stochastic Networks With Proportional Delay

Area of Science:

• Control Theory
• Artificial Intelligence
• Network Science

Background:

• Switched stochastic neural networks (SSNNs) are crucial for modeling complex dynamic systems.
• Proportional delay (PD) introduces unbounded time-varying delays, posing significant analytical challenges.
• Existing stability analysis methods often struggle with these complex delay characteristics.

Purpose of the Study:

• To investigate the exponential stability (ES) of SSNNs with PD.
• To develop novel methodologies for analyzing systems with unbounded time-varying delays.
• To establish new delay-dependent conditions for mean-square ES.

Main Methods:

• Utilizing the comparison principle and extended variation of parameters formula.
• Applying the average dwell-time (ADT) technique.
• Leveraging stochastic analysis theory and the Lyapunov approach.

Main Results:

• New delay-dependent conditions for mean-square ES are derived for the first time.
• The minimum average dwell time (MADT) is shown to depend on stable/unstable subsystems, decay ratio (DR), increasing ratio (IR), and PD.
• The analysis successfully addresses networks with both stable and unstable subsystems.

Conclusions:

• The developed methods provide a robust framework for analyzing SSNNs with PD.
• The findings enhance understanding of stability in complex neural network systems.
• Numerical simulations validate the effectiveness of the derived results under average dwell-time-switched regulation (ADTSR).