分数非线性微分系统的全球稳定性与依赖状态的延迟冲动
概括
这项研究引入了分数顺序非线性系统与状态依赖的延迟脉冲的稳定性的新标准. 这些发现为分析没有状态延迟边界性约束的复杂动态系统提供了新的方法.
科学领域:
- 动态系统理论 动态系统理论
- 非线性分析 非线性分析
- 控制理论 控制理论
背景情况:
- 分数顺序 (FO) 系统提供比整数顺序系统更准确的建模能力.
- 冲动效应和取决于国家的延迟在系统分析中带来了重大复杂性.
- 现有的稳定性分析方法通常需要对状态延迟进行限制,从而限制了适用性.
研究的目的:
- 开发分数级非线性微分系统的稳定性标准,这些系统具有依赖状态的延迟脉冲.
- 为卡普托的分数导数的单调性引入一个新的定理.
- 分析系统稳定性而不对状态延迟施加限制.
主要方法:
- 为卡普托的分数导数的单调性开发了一个新的定理.
- 应用线性矩阵不等式 (LMI) 技术.
- 在稳定性分析中使用比较论证.
主要成果:
- 建立了统一稳定性,统一非对称稳定性和米塔格-莱弗勒稳定性的标准.
- 展示了一种在没有状态延迟边界性的情况下对参数和冲动施加约束的方法.
- 通过两个说明性例子验证了理论分析.
结论:
- 提出的方法为分析复杂的分数级冲动系统的稳定性提供了有效的标准.
- 该方法放松了状态延迟局限性的常见约束,扩大了实际应用.
- 该研究有助于理论理解和分数顺序动态系统的实践分析.
相关概念视频
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01:28Stability
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The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
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01:18Second Order systems II
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01:21First Order Systems
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01:24BIBO stability of continuous and discrete -time systems
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01:26Linear Approximation in Frequency Domain
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