事件空间中Herglotz型Birkhoff参数方程的广义梯度实现及其稳定性分析

Generalized gradient realization and stability analysis of Herglotz-type Birkhoff’s parametric equations in event space

  • 摘要: 研究事件空间中Herglotz型Birkhoff系统的3类广义梯度表示及其稳定性. 首先,分别给出具有反对称矩阵、对称负定矩阵及半负定矩阵的广义梯度系统所对应的微分方程及其稳定性判据. 其次,推导将事件空间中Herglotz型Birkhoff系统的参数方程转化为上述3类广义梯度系统的条件. 在此基础上,利用广义梯度系统的性质,分析相应Herglotz型Birkhoff参数方程解的稳定性. 最后,通过算例验证所得结果的有效性.

     

    Abstract: This paper investigates three types of generalized gradient representations for Herglotz-type Birkhoffian systems in event space and their stability. First, the differential equations and corresponding stability criteria for generalized gradient systems characterized by antisymmetric, symmetric negative definite, and semi-negative definite matrices are presented, respectively. Secondly, the conditions under which the parametric equations of the Herglotz-type Birkhoffian systems in event space can be transformed into the aforementioned three types of generalized gradient systems are derived. Building upon this, the stability of solution for the corresponding Herglotz-type Birkhoffian parametric equations is analyzed by utilizing the properties of generalized gradient systems. Finally, the applicability of the obtained results is verified through specific examples.

     

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