通过弱CLCLF的交换正系统的基于图的限制和任意切换
IEEE transactions on cybernetics
|July 6, 2023
概括
这项研究确保了带有边际稳定的部分的离散时间切换正线性系统 (SPLS) 的稳定性. 微弱的共同线性共立的利亚普诺夫函数方法在各种切换信号下保证了非对称的稳定性.
科学领域:
- 控制系统工程 控制系统工程
- 系统理论 系统理论
- 应用数学 应用数学 应用数学
背景情况:
- 带有边际稳定的子系统的离散时间切换正线性系统 (SPLS) 存在独特的稳定性挑战.
- 在这样的系统中确保非对称稳定性需要先进的分析技术,这些分析技术既可以考虑系统动态,也可以考虑切换行为.
研究的目的:
- 调查和建立离散时间交换正线性系统 (SPLS) 与边际稳定的子系统的非对称稳定性的条件.
- 开发用于分析不同类型切换信号下的稳定性的新方法.
主要方法:
- 使用弱常规线性共立立普诺夫函数 (弱CLCLF) 方法.
- 将切换属性与状态组件属性结合起来.
- 开发循环依赖的联合路径条件,使用切换位图和状态组件位图进行转移受限切换.
- 在时间间隔序列下设计切换方案的路径条件的构建.
主要成果:
- 对于传输受限制的交换信号,提出了新的循环依赖的联合路径条件.
- 开发了两种类型的路径条件,用于在时间间隔序列下设计切换方案.
- 在任意切换下建立了对非对称稳定性的必要和充分条件.
结论:
- 建议的弱CLCLF方法有效地确保了带有边际稳定的子系统的SPLS的非对称稳定性.
- 开发的条件和方法为分析和设计稳定开关系统提供了强大的框架.
- 通过三个说明性示例来验证所介绍的方法的有效性.
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