Synchronization of Delayed Memristive Neural Networks: Robust Analysis Approach

Area of Science:

• Neuroscience
• Control Theory
• Nonlinear Dynamics

Background:

• Memristive Neural Networks (MNNs) exhibit state-dependent parameters, complicating traditional control methods.
• Time-varying delays introduce further challenges in analyzing MNN synchronization.
• Parameter mismatch issues arise due to differing initial conditions in MNNs.

Purpose of the Study:

• To investigate asymptotic and finite-time synchronization of drive-response MNNs with time-varying delays.
• To develop a robust control design that resolves parameter mismatch issues.
• To derive less conservative synchronization criteria compared to existing methods.

Main Methods:

• Utilizing the concept of Filippov solutions to handle state-dependent MNN parameters.
• Designing a new robust control strategy to address parameter mismatch.
• Deriving sufficient conditions for asymptotic synchronization.
• Investigating finite-time synchronization without relying on existing finite-time stability theorems.

Main Results:

• Sufficient conditions for asymptotic synchronization of MNNs with time-varying delays were established.
• The proposed synchronization criteria are potentially less conservative than existing methods.
• Finite-time synchronization of MNNs with delays was successfully investigated.
• Numerical simulations validated the effectiveness of the developed theoretical analysis.

Conclusions:

• The study provides effective methods for achieving both asymptotic and finite-time synchronization in complex MNNs.
• The novel robust control design successfully tackles parameter mismatch issues.
• The findings offer a valuable contribution to the field of MNNs synchronization and control.