Exponential State Estimation for Memristor-Based Discrete-Time BAM Neural Networks With Additive Delay Components

Area of Science:

• Neural Networks
• Control Theory
• Dynamical Systems

Background:

• Memristor-based bidirectional associative memory neural networks (BAMNNs) are crucial for associative memory tasks.
• Time-varying delays in discrete-time systems can destabilize network dynamics.
• State estimation is vital for monitoring and controlling complex neural network systems.

Purpose of the Study:

• To design a state estimator for discrete-time memristor-based BAMNNs with time-varying delays.
• To ensure the exponential stability of the estimation error dynamics with a prescribed decay rate.
• To develop delay-dependent conditions for the existence of the state estimator.

Main Methods:

• Construction of a Lyapunov-Krasovskii functional (LKF).
• Application of Cauchy-Schwartz-based summation inequality.
• Formulation of delay-dependent sufficient conditions using linear matrix inequalities (LMIs).
• Extension of conditions to handle uncertain parameters within the BAMNNs.

Main Results:

• Sufficient conditions for the existence of the state estimator are derived.
• Conditions are presented in terms of LMIs, allowing for computational solutions.
• Estimation gain matrices are obtained by solving the derived LMI conditions.
• The effectiveness of the proposed method is demonstrated through two numerical examples.

Conclusions:

• The proposed method effectively designs state estimators for memristor-based BAMNNs with time-varying delays.
• The derived LMI conditions provide a systematic approach to achieve stable estimation error dynamics.
• The results contribute to the robust control and analysis of complex neural network models.