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This chapter provides another perspective of the long-time behavior of switching diffusions by focusing on stability of an equilibrium point. Suffcient conditions for stability and instability in probability, exponential p-stability and almost sure exponential stability are presented. Moreover, easily verifiable conditions for stability and instability of linearized systems are provided. The main machineries are Lyapunov function methods.

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Stability

  • 章节

  • 发表日期：

    2025年

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  • Hai-Dang Nguyen,
  • George Yin,
  • Chao Zhu

摘要

This chapter provides another perspective of the long-time behavior of switching diffusions by focusing on stability of an equilibrium point. Suffcient conditions for stability and instability in probability, exponential p-stability and almost sure exponential stability are presented. Moreover, easily verifiable conditions for stability and instability of linearized systems are provided. The main machineries are Lyapunov function methods.