Stability criteria for singularly perturbed impulsive linear switched systems

2025/07/03 by Ihab Haidar, Yacine Chitour, Haidar, Ihab +7
Mathematics · Computer Science · #Differential Equations and Numerical Methods #Mathematical Control Systems and Analysis #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2507.02446

Abstract

We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove that the stability or instability of these auxiliary systems directly determines that of the original system in the regime of small singular perturbation parameters.

Citations

• Singularly Perturbed Hybrid Systems for Analysis of Networks With Frequently Switching Graphs
• Stabilization of singularly perturbed networked control systems over a single channel
• Upper and lower bounds for the maximal Lyapunov exponent of singularly perturbed linear switching systems
• A Lyapunov framework for nested dynamical systems on multiple time\n scales with application to converter-based power systems
• Stability analysis of a general class of singularly perturbed linear hybrid systems

Related

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