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Delay-dependent global exponential robust stability for delayed cellular neural networks with time-varying delay.

¹Department of Automation Engineering Institute of Mechatronoptic System, Chienkuo Technology University, Changhua 500, Taiwan, ROC.

ISA Transactions

|July 23, 2013

Summary

This study presents a new method for analyzing stability in delayed cellular neural networks (DCNN) with time-varying delays. The approach uses a linear matrix inequality (LMI) for simpler, less conservative stability analysis.

Keywords:

Delayed cellular neural networks (DCNN)Exponential stability Linear matrix inequality (LMI)Lyapunov–Krasovskii functional Time-varying delays

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Area of Science:

Control Systems Engineering
Computational Neuroscience
Nonlinear Dynamics

Background:

Delayed Cellular Neural Networks (DCNN) are crucial for modeling complex systems.
Stability analysis of DCNN with time-varying delays presents significant challenges.
Existing methods often yield conservative results or are computationally intensive.

Purpose of the Study:

To develop a novel, less conservative criterion for the uniform asymptotic stability of DCNN with time-varying delays.
To formulate the stability condition using a single Linear Matrix Inequality (LMI).
To account for the derivative of the time-varying delay, even when its upper bound is greater than or equal to 1.

Main Methods:

Lyapunov-Krasovski functional approach.
Integral Inequality Approach (IIA).
Formulation of stability conditions as a single Linear Matrix Inequality (LMI).
Convex optimization techniques for solving the LMI.

Main Results:

A new criterion for uniform asymptotic stability of DCNN with time-varying delays is derived.
The criterion is expressed as a single, easily solvable LMI.
The proposed method is less conservative than existing techniques, especially when considering the delay derivative.
Numerical examples demonstrate the effectiveness and reduced conservatism of the proposed method.

Conclusions:

The developed LMI-based criterion provides an efficient and less conservative approach for analyzing the stability of DCNN with time-varying delays.
The method's ability to handle larger delay derivatives enhances its applicability.
The findings contribute to the robust design and analysis of complex neural network systems.