与α∈(0,+∞) 的三角形分数顺序系统的明确稳定性条件
Yiheng Wei1, Shuaiyu Zhou1, YangQuan Chen2
1School of Mathematics, Southeast University, Nanjing 211189, China.
ISA transactions
|May 14, 2024
概括
本研究分析了超出典型的 (0,1) 范围的时间提前三角形分数顺序系统的稳定性. 它提供了基于自身值分布的明确稳定性条件,并通过示例验证.
科学领域:
- 控制系统工程 控制系统工程
- 分数微积分的计算.
- 动态系统分析 动态系统分析
背景情况:
- 分数顺序系统在模拟复杂现象时越来越重要.
- 对于分数系统的传统稳定性分析通常仅限于0和1之间的顺序.
- 时间提前的三角形分数顺序系统需要专门的稳定性调查方法.
研究的目的:
- 调查时间提前的三角形分数订单系统的稳定性,用于范围内的订单 (0,+∞).
- 为这些系统推导一个明确的稳定性条件.
- 分析不稳定的地区的特点.
主要方法:
- 达尔塔拉普拉斯变换用于稳定性分析的应用.
- 引入一个映射关系 ρ=s/(s+1).
- 确定delta和nabla差异运算符之间的等价性.
- 系统矩阵的自身价值分布分析.
主要成果:
- 对于时间提前的三角形分数顺序系统来说,一个明确的稳定性条件是导出的.
- 该条件与系统矩阵的固有值直接相关.
- 定量和定性分析揭示了这个不稳定的地区的范围.
结论:
- 开发的稳定性条件通过三个说明性示例严格验证.
- 这些发现扩大了对分数顺序系统稳定性的理解,超出了传统的限制.
- 德尔塔和纳布拉差异之间的等价性有助于验证结果.
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