Input-to-state stability of stochastic nonlinear system with delayed impulses
1School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China.
Mathematical Biosciences and Engineering : MBE
|March 8, 2024
Summary
This study establishes theoretical conditions for stochastic input-to-state stability (SISS) in nonlinear systems with delayed impulses. The findings address systems with stable, unstable, and multiple impulse jumps, validating results with numerical examples.
Area of Science:
- Control Theory
- Nonlinear Systems
- Stochastic Systems
Background:
- Stochastic input-to-state stability (SISS) is crucial for analyzing nonlinear systems.
- Impulsive effects and time delays introduce significant complexity in system stability analysis.
Purpose of the Study:
- To investigate the SISS of stochastic nonlinear systems with delayed impulses.
- To develop theoretical conditions for ensuring SISS under various system configurations.
- To explore SISS for systems with both stable and unstable subsystems and multiple delayed impulse jumps.
Main Methods:
- Utilizing the average impulsive interval method.
- Applying the Lyapunov approach for stability analysis.
- Considering a positively time-varying Lyapunov rate coefficient.
Main Results:
- Established theoretical conditions for SISS in systems with stable subsystems and delayed impulses.
- Analyzed SISS characteristics for augmented systems containing both stable and unstable subsystems.
- Explored SISS properties for stochastic nonlinear systems with multiple delayed impulse jumps.
Conclusions:
- The developed theoretical conditions are effective in ensuring SISS for the studied systems.
- The Lyapunov approach combined with the average impulsive interval method provides a robust framework for stability analysis.
- Numerical examples validate the theoretical findings, confirming the system's SISS properties.
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