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Stochastic Practical Fixed-Time Input-to-State Stability and Its Applications
IEEE Transactions on Cybernetics
|July 27, 2026
Summary
This study introduces stochastic practical fixed-time input-to-state stability (SPFT-ISS) and its associated Lyapunov function. This framework is applied to solve adaptive control problems for complex stochastic nonlinear systems.
Area of Science:
- Control Theory
- Stochastic Systems
- Nonlinear Dynamics
Background:
- Stability analysis is crucial for control systems.
- Fixed-time stability offers finite-time convergence guarantees.
- Stochastic systems introduce inherent randomness.
Purpose of the Study:
- To establish a comprehensive framework for stochastic practical fixed-time input-to-state stability (SPFT-ISS).
- To introduce the concept of stochastic practical fixed-time stability (SPFTS).
- To apply the developed framework to adaptive control of stochastic nonlinear systems.
Main Methods:
- Development of the SPFT-ISS framework.
- Introduction and definition of SPFTS.
- Utilizing SPFT-ISS Lyapunov functions for stability analysis.
- Designing adaptive controllers for systems with uncertainties.
Main Results:
- The SPFT-ISS framework and SPFTS concept are formally proposed.
- The relationship between SPFT-ISS and its Lyapunov function is established.
- A thorough solution for adaptive practical fixed-time control of challenging stochastic nonlinear systems is presented.
Conclusions:
- The proposed SPFT-ISS framework provides a robust tool for analyzing and controlling stochastic systems.
- The adaptive control solution demonstrates the practical applicability of the framework.
- This work advances the understanding of stability and control for stochastic nonlinear systems.
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