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Updated: Jul 21, 2025
08:07
Assembly and Characterization of Biomolecular Memristors Consisting of Ion Channel-doped Lipid Membranes
Published on: March 9, 2019
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$ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive NNs with non-necessarily differentiable time-varying
1School of Computer Science and Technology, Anhui University of Technology, Ma'anshan 243032, China.
Mathematical Biosciences and Engineering : MBE
|July 28, 2023
Summary
This study introduces robust control for memristive neural networks (MNNs) with time-varying delays. It ensures stability using novel Lyapunov-based methods and linear matrix inequalities for controller design.
Area of Science:
- Control Theory
- Neural Networks
- Nonlinear Systems
Background:
- Memristive neural networks (MNNs) are crucial for complex computations.
- Time-varying delays in MNNs introduce stability challenges.
- Robust control is essential for reliable MNN performance.
Purpose of the Study:
- To design an output-feedback controller for MNNs with non-differentiable time-varying delays.
- To ensure the $\mathcal{L}_2 -\mathcal{L}_{\infty}$ stability of the MNN system.
- To develop a systematic design method for the controller.
Main Methods:
- Utilizing a Lyapunov functional for stability analysis.
- Applying the Bessel-Legendre inequality and convex combination inequality.
- Employing linear matrix inequalities (LMIs) for controller synthesis.
- Decoupling nonlinear terms within the MNN dynamics.
Main Results:
- A novel criterion for $\mathcal{L}_2 -\mathcal{L}_{\infty}$ stability of MNNs with delays is established.
- A concrete LMI-based design scheme for the output-feedback controller is presented.
- The proposed methods are validated through two illustrative examples.
Conclusions:
- The developed $\mathcal{L}_2 -\mathcal{L}_{\infty}$ stability criterion is effective for MNNs with delays.
- The LMI-based controller design ensures system stability and performance.
- This research contributes to the robust control of complex neural network systems.
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