Finite-time stabilization control for discontinuous time-delayed networks: New switching design

Area of Science:

• Control Theory
• Computational Neuroscience
• Dynamical Systems

Background:

• Neural networks with time delays (DNNs) are crucial for modeling complex systems.
• Discontinuous activation functions and time-varying delays present significant challenges in stability analysis.
• Finite-time stabilization is essential for practical applications requiring rapid response.

Purpose of the Study:

• To investigate the finite-time stabilization problem for time-varying delayed neural networks with discontinuous activation functions.
• To develop novel switching controllers for achieving finite-time stabilization.
• To establish theoretical criteria and estimate settling times for stabilization.

Main Methods:

• Utilizing fixed point theory and set-valued analysis to establish the existence of equilibrium points.
• Designing two types of discontinuous switching controllers.
• Applying Filippov's theory of differential inclusions for discontinuous systems.
• Leveraging finite-time stability theory to derive stabilization criteria.

Main Results:

• Existence theorem for equilibrium points in discontinuous DNNs established.
• New criteria for finite-time stabilization of discontinuous DNNs derived under Filippov solutions.
• Two distinct switching controllers designed for effective stabilization.
• Upper bounds for the settling time of stabilization are estimated.

Conclusions:

• The proposed switching controllers effectively achieve finite-time stabilization for the studied class of DNNs.
• The derived criteria provide a robust framework for analyzing and ensuring stability.
• Numerical examples validate the efficacy of the theoretical results and design methodology.