Mixed-Delay-Based Augmented Functional for Sampled-Data Synchronization of Delayed Neural Networks With Communication...

Area of Science:

• Control Theory
• Neural Networks
• Systems Engineering

Background:

• Delayed Neural Networks (DNNs) are crucial in modeling complex systems.
• Existing research on DNN synchronization often overlooks the interplay between transmission and communication delays.
• Time-squared terms in Lyapunov functionals are frequently underutilized, limiting analytical precision.

Purpose of the Study:

• To investigate the synchronization control of DNNs with sampled-data controllers under communication delay.
• To clarify the interaction between transmission delay and communication delay in DNN synchronization.
• To develop a less conservative synchronization criterion by addressing underutilized time-squared terms.

Main Methods:

• A novel augmented Lyapunov functional is proposed, incorporating a mixed-delay-based part and a time-squared two-sided looped part.
• The mixed-delay part explicitly considers the interaction between transmission and communication delays.
• The time-squared part integrates time-dependent quadratic terms and sampling integral states to capture sampling pattern characteristics.

Main Results:

• A new augmented Lyapunov functional is designed to effectively handle mixed delays and sampling characteristics.
• The proposed method yields a less conservative synchronization criterion for DNNs.
• The criterion is formulated in the form of linear matrix inequalities (LMIs).

Conclusions:

• The developed synchronization criterion is valid and superior, as demonstrated by a numerical example.
• The novel Lyapunov functional effectively addresses the complexities of transmission and communication delays in DNN synchronization.
• This research advances the control of networked systems with time delays.