Stability and L2 performance analysis of stochastic delayed neural networks

Area of Science:

• Control Theory
• Stochastic Systems
• Neural Networks

Background:

• Time-delay neural networks are crucial in modeling complex systems.
• Stochastic perturbations (additive and multiplicative) introduce significant challenges in stability analysis.
• Ensuring robust mean-square exponential stability and L(2) performance is vital for reliable system operation.

Purpose of the Study:

• To develop novel criteria for analyzing the robust mean-square exponential stability of uncertain time-delay neural networks.
• To establish criteria for L(2) performance analysis under combined stochastic noises.
• To present a method that is less conservative and computationally efficient than existing approaches.

Main Methods:

• Utilizing the delay partition Lyapunov-Krasovskii functional method.
• Applying the generalized Finsler lemma, specifically adapted for stochastic systems.
• Developing analytical results without requiring model transformations or additional parameters.

Main Results:

• New criteria for mean-square exponential stability and L(2) performance were successfully derived.
• The proposed method avoids common complexities like cross-term estimations and free-weighting matrices.
• Numerical examples demonstrate the effectiveness and reduced conservatism of the developed approach.

Conclusions:

• The developed criteria provide a robust framework for analyzing uncertain time-delay neural networks with stochastic disturbances.
• The method offers significant advantages in terms of reduced conservatism and computational load.
• This work contributes to the reliable design and analysis of stochastic neural network systems.