イベントトリガーインパルス制御による分散遅延インパルスによる非線形ストカスティックシステムの安定性
1School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China.
Mathematical biosciences and engineering : MBE
|September 3, 2025
まとめ
この研究は,遅延を持つ非線形ストキャスティックシステムに対するイベントトリガードインパルス制御 (ETIC) を導入します. LMIと数値的な例によって検証された新しいメカニズムが安定性を確保し,Zenoの行動を防止します.
科学分野:
- 制御理論
- 非線形システム
- ストキャスティック・システム
背景:
- 複雑なダイナミクスを管理するために,衝動的な制御システムは不可欠です.
- 分布された遅延とストキャスティシティは,重要な安定性課題をもたらします.
- イベントトリガードインパルス制御 (ETIC) は効率的なデータ伝送を提供します.
研究 の 目的:
- ETICの下で分散遅延インパルスを持つ非線形ストキャスティックシステムの安定性を調査する.
- ゼロノの行動を回避する新しい連続的および周期的なイベントトリガーメカニズム (ETM) を提案する.
- p-thモメントの均等な安定性 (p-US) とp-thモメントの指数的な安定性 (p-ES) のための十分な条件を確立する.
主な方法:
- 安定分析のためのリヤプノフ法と数学的誘導.
- 継続的および周期的なイベントトリガーメカニズム (ETM) の開発.
- ETMと制御の共同設計のための線形マトリックス不平等 (LMI) アプローチ.
主要な成果:
- 分散遅延インパルスを持つシステムでp-USとp-ESを確保するために十分な条件を導出します.
- 提案されたETMはZenoの行動を効果的に排除します.
- 非線形ストキャスティックシステムへの応用が成功し,数値的な例によって実現可能性が示された.
結論:
- 提案されたETICフレームワークは,分散された遅延を持つ非線形ストキャスティックシステムの安定化のための堅固な方法を提供します.
- LMIを使用した結合設計は,効果的な制御と安定性を保証します.
- 数学的シミュレーションは,理論的な発見の実用性と有効性を確認します.
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