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Practical Exponential Stability of Impulsive Stochastic Reaction-Diffusion Systems With Delays
IEEE Transactions on Cybernetics
|October 1, 2020
Summary
This study investigates practical exponential stability for impulsive stochastic reaction-diffusion systems with delays. The developed methods effectively analyze and ensure system stability, offering valuable stabilization results.
Area of Science:
- Stochastic Systems
- Control Theory
- Dynamical Systems
Background:
- Impulsive stochastic reaction-diffusion systems (ISRDSs) with delays present complex dynamics.
- Ensuring practical exponential stability is crucial for reliable system performance.
- Existing methods may not fully address the challenges posed by delays and impulses.
Purpose of the Study:
- To develop and apply novel methods for analyzing the p th moment practical exponential stability of ISRDSs with delays.
- To estimate the convergence rate of these systems.
- To demonstrate the applicability of these methods to impulsive reaction-diffusion stochastic Hopfield neural networks (IRDSHNNs) with delays.
Main Methods:
- A direct approach is employed to investigate practical exponential stability.
- The Lyapunov method is utilized for stability analysis and convergence rate estimation.
- The developed techniques are applied to specific models like IRDSHNNs.
Main Results:
- The study establishes criteria for p th moment practical exponential stability in ISRDSs with delays.
- Convergence rates for the systems are effectively estimated.
- The practical stability results are validated through successful application to IRDSHNNs.
Conclusions:
- The developed direct and Lyapunov methods are effective for analyzing practical exponential stability in ISRDSs with delays.
- The findings provide valuable stabilization results for these complex systems.
- Numerical examples confirm the efficacy of the proposed approaches.
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