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Multiple generalized stability of nonlinear delayed systems subject to impulsive disturbance
Fanghai Zhang1, Changlin Zhan1
1School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, 230009, Anhui China.
Cognitive Neurodynamics
|April 22, 2025
Summary
This study investigates the generalized stability of nonlinear systems with impulsive disturbances and distributed delays. We provide conditions for the stability of multiple equilibrium points in these complex systems.
Area of Science:
- Control theory
- Nonlinear dynamics
- Systems analysis
Background:
- Nonlinear systems are prevalent in science and engineering.
- Impulsive disturbances and distributed delays introduce significant complexity in system analysis.
- Understanding generalized stability is crucial for reliable system design.
Purpose of the Study:
- To investigate the multiple generalized stability of nonlinear systems.
- To analyze systems affected by impulsive disturbances and distributed delays.
- To derive conditions for the stability of multiple equilibrium points.
Main Methods:
- State space partition method.
- Mathematical analysis of nonlinear systems.
- Derivation of sufficient conditions for stability.
Main Results:
- The number of multiple equilibrium points for an n-dimensional system is determined.
- Sufficient conditions for the generalized stability of multiple equilibrium points are established.
- Theoretical results are validated through simulation examples.
Conclusions:
- The proposed methods provide a framework for analyzing the generalized stability of complex nonlinear systems.
- The derived conditions enhance the understanding of system behavior under impulsive disturbances and delays.
- The findings have implications for the design and control of robust nonlinear systems.
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