Research Paper#Control Theory, Stochastic Systems, Hybrid Systems🔬 ResearchAnalyzed: Jan 3, 2026 19:34
Stability Analysis of Singularly Perturbed Stochastic Hybrid Systems
Analysis
This paper addresses the challenging problem of analyzing the stability and recurrence properties of complex dynamical systems that combine continuous and discrete dynamics, subject to stochastic disturbances and multiple time scales. The use of composite Foster functions is a key contribution, allowing for the decomposition of the problem into simpler subsystems. The applications mentioned suggest the relevance of the work to various engineering and optimization problems.
Key Takeaways
- •Focuses on stability and recurrence of singularly perturbed stochastic hybrid systems.
- •Employs composite Foster functions for analysis.
- •Applies to systems with multi-time-scale dynamics, stochastic disturbances, and hybrid behavior.
- •Provides examples in switching systems, feedback optimization, and momentum-based optimization.
Reference
“The paper develops a family of composite nonsmooth Lagrange-Foster and Lyapunov-Foster functions that certify stability and recurrence properties by leveraging simpler functions related to the slow and fast subsystems.”