ストキャスティック構造の非線形不確実性のクラスの下での離散時間マルコフジャンプ線形システムの堅固な安定性と堅固な安定化
Vasile Dragan1,2, Samir Aberkane3
1Institute of Mathematics "Simion Stoilow" of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania.
Entropy (Basel, Switzerland)
|August 28, 2025
まとめ
この研究は,パラメータの乱れを持つ離散時間マルコフジャンプ線形システムの堅固な安定化に取り組んでいます. 安定半径の下限を設定します これは信頼性の高い制御システムの設計に不可欠です
科学分野:
- 制御システム工学
- システム理論
- ストキャスティック・システム
背景:
- マルコビアンジャンプ・リニアシステム (MJLS) は,急激な変化を伴うシステムをモデル化するために広く使用されています.
- パラメータの不確実性とストキャスティックな混乱は,システムの安定性と制御に重大な課題をもたらす.
- 強力な安定性を確保することは,ダイナミックシステムの信頼性の高い動作に不可欠です.
研究 の 目的:
- ブロック対角のストキャスティックパラメータによる離散時間,時間変動のMJLSの堅固な安定性と安定化を調査する.
- 多動のシナリオで安定半径を推定する方法を開発する.
- これらのシステムの強固な安定化問題に対処します.
主な方法:
- マルチパルバーバーションを効果的に処理するためにスケーリング技術が使用されます.
- 安定半径の下限は,パラメータ化された逆のリヤプノフ差方程式を使用して導出されます.
- 分析は時間変数と時間不変数の両方に広がります.
主要な成果:
- 安定半径の下限を推定する.
- 時間不変系では,この下限が正確な安定半径であることが示されています.
- 開発された結果は,国家フィードバックの堅固な安定化問題の解決を容易にする.
結論:
- 提案された方法は,混乱したMJLSの堅固な安定化に効果的に取り組んでいます.
- 安定半径の推定は,システムの頑丈さのための貴重なメトリックを提供します.
- この発見は,不確実性のある制御システムの設計に寄与します.
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