Operator-Theoretic Study on the Synthesis and Analysis of Control Systems via Fast-Lifting and Its Algebraic Extension

• Project/Area Number: 21560461
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Control engineering
• Research Institution: Kyoto University
• Principal Investigator: HAGIWARA Tomomichi 京都大学, 大学院・工学研究科, 教授 (70189463)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 高速リフティング / サンプル値系 / むだ時間系 / モノドロミー作用素 / 非因果的 / 離散時間系 / 周期時変スケーリング / 準有限ランク近似 / 伸張型LMI / シフト不変性 / サンプル値

Research Abstract

The study dealt with a basic tool called fast-lifting that plays a significant role in advanced treatment in the synthesis and analysis of control systems employing digital devices or involving transportation of material, information, energy and so on. It mathematically tackles this tool from an operator-theoretic viewpoint, and further studies extensions of simplified ideas so that they can be applied to other types of control systems.

Research Products

• [Journal Article] Block Checker/Diagonal Transformation Matrices, Their Properties, and the Interplay with Fast-Lifting (2011)
  • Author(s): T. Hagiwara
  • Journal Title: International Journal of Systems Science Volume: Vol.42, No.8 Pages: 1293-1303
  • URL: http://www.tandfonline.com/doi/abs/10.1080/00207721.2010.496057
  • Peer Reviewed
• [Journal Article] Properties of Discrete-Time Noncausal Linear Periodically Time-Varying Scaling and Their Relation-ship with Shift-Invariance in Lifting-Timing (2011)
  • Author(s): Y. Hosoe and T. Hagiwara
  • Journal Title: International Journal of Control Volume: Vol.84, No.6 Pages: 1067-1079
  • URL: http://www.tandfonline.com/doi/abs/10.1080/00207179.2011.591432
  • Peer Reviewed
• [Journal Article] Fast-Lifting Approach to the Computation of the Spectrum of Retarded Time-Delay Systems (2011)
  • Author(s): T. Hagiwara and K. Hirata
  • Journal Title: European Journal of Control Volume: Vol.17, No.2 Pages: 162-171
  • URL: http://ejc.revuesonline.com/article.jsp?articleId=16019
  • Peer Reviewed
• [Journal Article] Noncausal Linear Periodically Time-Varying Scaling for Robust Stability Analysis of Discrete-Time Systems : Frequency-Dependent Scaling In-duced by Static Separators (2011)
  • Author(s): T. Hagiwara and Y. Ohara
  • Journal Title: Automatica Volume: Vol.46, No.1 Pages: 167-173
  • URL: http://dx.doi.org/10.1016/j.automatica.2009.10.019
  • Peer Reviewed
• [Journal Article] Fast-Lifting Approach to the Computation of the Spectrum of Retarded Time-Delay Systems (2011)
  • Author(s): T.Hagiwara
  • Journal Title: European Journal of Control Volume: 17 Pages: 162-171
  • Peer Reviewed
• [Journal Article] Properties of Discrete-Time Noncausal Linear Periodically Time-Varying Scaling and Their Relationship with Shift-Invariance in Lifting-Timing (2011)
  • Author(s): Y.Hosoe
  • Journal Title: International Journal of Control Volume: 84 Issue: 6 Pages: 1067-1079
  • DOI: 10.1080/00207179.2011.591432
  • Peer Reviewed
• [Journal Article] Block Checker/Diagonal Transformation Matrices, Their Properties, and the Interplay with Fast-Lifting (2011)
  • Author(s): T.Hagiwara
  • Journal Title: International Journal of Systems Science Volume: 42 Issue: 8 Pages: 1293-1303
  • DOI: 10.1080/00207721.2010.496057
  • Peer Reviewed
• [Journal Article] Quasi-Finite-Rank Approximation of Com-pression Operators in Sampled-Data Systems and Time-Delay Systems (2010)
  • Author(s): T. Hagiwara, K. Morioka and K. Okada
  • Journal Title: International Journal of Control Volume: Vol.83, No.11 Pages: 2385-2394
  • URL: http://dx.doi.org/10.1080/00207179.2010.523849
  • Peer Reviewed
• [Journal Article] Stability Analysis of Sampled-Data Systems with Static Sector Nonlinearities via Causal Linear Periodically Time-Varying Scal-ing (2010)
  • Author(s): K. Morioka and T. Hagiwara
  • Journal Title: SICE Journal on Control, Measure-ment, and System Integration Volume: Vol.3, No.4 Pages: 260-265
  • URL: http://www.jstage.jst.go.jp/article/jcmsi/3/4/3260/article/
  • Peer Reviewed
• [Journal Article] 離散時間非因果的周期時変スケーリングに基づくロバスト安定化制御器設計 (2010)
  • Author(s): 細江陽平, 萩原朋道
  • Journal Title: 計測自動制御学会論文集 Volume: Vol.46, No.4 Pages: 219-228
  • NAID: 10026208065
  • URL: http://www.jstage.jst.go.jp/article/sicetr/46/4/46219/article/-char/ja
  • Peer Reviewed
• [Journal Article] Noncausal Linear Periodically Time-Varying Scaling for Robust Stability Analysis of Discrete-Time Systems : Frequency-Dependent Scaling Induced by Static Separators (2010)
  • Author(s): T.Hagiwara, Y.Ohara
  • Journal Title: Automatica Volume: 46-1 Pages: 167-173
  • Peer Reviewed
• [Journal Article] 離散時間非因果的周期時変スケーリングに基づくロバスト安定化制御器設計 (2010)
  • Author(s): 細江陽平・萩原朋道
  • Journal Title: 計測自動制御学会論文集 Volume: 46-4 Pages: 219-228
  • NAID: 10026208065
  • Peer Reviewed
• [Journal Article] Stability Analysis of Sampled-Data Systems with Static Sector Nonlinearities via Causal Linear Periodically Time-Varying Scaling (2010)
  • Author(s): K.Morioka, T.Hagiwara
  • Journal Title: SICE Journal on Control, Measurement and System Integration Volume: 3-4 Pages: 260-265
  • NAID: 10031140014
  • Peer Reviewed
• [Journal Article] Quasi-Finite-Rank Approximation of Compression Operators in Sampled-Data Systems and Time-Delay Systems (2010)
  • Author(s): T.Hagiwara, K.Morioka, K.Okada
  • Journal Title: International Journal of Control Volume: 83-11 Pages: 2385-2394
  • Peer Reviewed
• [Journal Article] Modified Fast-Sample/Fast-Hold Approximation and γ-independent H∞-discretisation for General Sampled-Data Systems by Fast-Lifting (2009)
  • Author(s): T.Hagiwara, K.Okada
  • Journal Title: International Journal of Control 82-9 Pages: 1762-1771
  • NAID: 120002317397
  • Peer Reviewed
• [Journal Article] Separator-type Robust Stability Theorem of Sampled-data Systems Allowing Noncausal LPTV Scaling (2009)
  • Author(s): T.Hagiwara
  • Journal Title: Automatica 45-8 Pages: 1868-1872
  • NAID: 120001462501
  • Peer Reviewed
• [Journal Article] Noncausal Linear Periodically Time-varying Scaling for Robust Stability Analysis of Discrete-time Systems : Frequency-dependent Scaling Induced by Static Separators (2009)
  • Author(s): T.Hagiwara, Y.Ohara
  • Journal Title: Automatica 46-1 Pages: 167-173
  • Peer Reviewed
• [Presentation] Infinite Matrix Representations of Robust Stability Conditions for Discrete-Time Systems (2012)
  • Author(s): T.Hagiwara
  • Organizer: 2011 50th IEEE Conference on Decision and Control and European Control Conference
  • Place of Presentation: オーランド
  • Year and Date: 2012-12-13
• [Presentation] 構造的不確かさの動的要素に対するFIRスケーリングの活用 (2012)
  • Author(s): 萩原朋道
  • Organizer: 計測自動制御学会第12回制御部門大会
  • Place of Presentation: 奈良県文化会館
  • Year and Date: 2012-03-15
• [Presentation] L∞[O,h]誘導ノルムに基づくcompression作用素の準有限ランク近似 (2012)
  • Author(s): 萩原朋道
  • Organizer: 計測自動制御学会第12回制御部門大会
  • Place of Presentation: 奈良県文化会館
  • Year and Date: 2012-03-15
• [Presentation] Infinite Ma-trix Representations of Robust Stability Con-ditions for Discrete-Time Systems (2011)
  • Author(s): Y. Hosoe and T. Hagiwara
  • Organizer: 2011 50th IEEE Conference on Decision and Control and European Control Conference
  • Place of Presentation: Orlando
  • Year and Date: 2011-12-13
• [Presentation] A Note on Separator-Type Robust stability Theorem and Well-Posedness of Linear Time-Invariant Systems (2011)
  • Author(s): T.Hagiwara
  • Organizer: 2011 Australian Control Conference
  • Place of Presentation: メルボルン
  • Year and Date: 2011-11-11
• [Presentation] A Note on Separator-Type Robust stability Theorem and Well-Posedness of Linear Time-Invariant Systems (2011)
  • Author(s): T. Hagiwara
  • Organizer: 2011 Australian Control Conference
  • Place of Presentation: Merbourne
  • Year and Date: 2011-11-10
• [Presentation] 離散時間FIRスケーリングに基づくロバスト安定解析 (2011)
  • Author(s): 萩原朋道
  • Organizer: 計測自動制御学会第40回制御理論シンポジウム
  • Place of Presentation: コスモスクウェア国際交流センター
  • Year and Date: 2011-09-27
• [Presentation] Robust Stability Analysis with Cycling-Based LPTV Scaling and Its Relationship with Lifting-Based Approach (2011)
  • Author(s): T.Hagiwara
  • Organizer: SICE Annual Conference 2011
  • Place of Presentation: 早稲田大学
  • Year and Date: 2011-09-16
• [Presentation] Relationship between Noncausal Linear Periodically Time-Varying Scaling and Causal Linear Time-Invariant Scaling for Discrete-Time Systems (2011)
  • Author(s): T.Hagiwara
  • Organizer: 18^<th> IFAC World Congress
  • Place of Presentation: ミラノ
  • Year and Date: 2011-08-29
• [Presentation] Fast-Lifting Approach to the Computation of the Spectral Radius of Neutral Time-Delay Sys-tems (2011)
  • Author(s): T. Hagiwara and T. Fujinami
  • Organizer: IFAC Workshop on Time Delay Sys-tems
  • Place of Presentation: Prague
  • Year and Date: 2011-06-08
• [Presentation] 集中定数部の累乗に対する有限ランク近似に基づくむだ時間系の安定解析法 (2011)
  • Author(s): 萩原朋道
  • Organizer: 第55回システム制御情報学会研究発表講演会
  • Place of Presentation: 大阪大学
  • Year and Date: 2011-05-11
• [Presentation] ポリトープ型不確かさを含むサンプル値系の高速リフティングに基づくロバスト安定解析 (2011)
  • Author(s): 萩原朋道
  • Organizer: 第55回システム制御情報学会研究発表講演会
  • Place of Presentation: 大阪大学
  • Year and Date: 2011-05-11
• [Presentation] Synthesis of robust performance controllers based on discrete-time noncausal linear periodically time-varying scaling (2010)
  • Author(s): Y.Hosoe, T.Hagiwara
  • Organizer: IFAC Workshop on Periodic Control Systems
  • Place of Presentation: Antalya, Turkey
  • Year and Date: 2010-08-27
• [Presentation] Effects induced by noncausality of scaling on robust stability analysis of discrete-time periodically time-varying systems (2010)
  • Author(s): Y.Hosoe, T.Hagiwara
  • Organizer: 2010 SICE Annual Conference
  • Place of Presentation: Taipei
  • Year and Date: 2010-08-19
• [Presentation] Monodromy Op-erator Approach to Time-Delay Systems : Nu-merical Method for Solving Operator Lya-punov Inequalities (2010)
  • Author(s): T. Hagiwara and T. Inui
  • Organizer: 19th International Sym-posium on Mathematical Theory of Networks and Systems
  • Place of Presentation: Budapest
  • Year and Date: 2010-07-07
• [Presentation] Monodromy Operator Ap-proach to Time-Delay Systems : Fast-Lifting Based Treatment of Operator Lyapunov In-equalities (2010)
  • Author(s): T. Hagiwara
  • Organizer: 19th International Symposium on Mathematical Theory of Networks and Sys-tems
  • Place of Presentation: Budapest
  • Year and Date: 2010-07-07
• [Presentation] Monodromy operator approach to time-delay systems : fast-lifting based treatment of operator Lyapunov inequalities (2010)
  • Author(s): T.Hagiwara
  • Organizer: 19^<th> International Symposium on Mathematical Theory of Networks and Systems
  • Place of Presentation: Budapest
  • Year and Date: 2010-07-06
• [Presentation] Monodromy operator approach to time-delay systems : numerical method for solving operator Lyapunov inequalities (2010)
  • Author(s): T.Hagiwara, T.Inui
  • Organizer: 19^<th> International Symposium on Mathematical Theory of Networks and Systems
  • Place of Presentation: Budapest
  • Year and Date: 2010-07-06
• [Presentation] Fast-lifting approach to the computation of the spectral radius of neutral time-delay systems (2010)
  • Author(s): T.Hagiwara, T.Fujinami
  • Organizer: IFAC Workshop on Time-Delay Systems
  • Place of Presentation: Prague
  • Year and Date: 2010-06-07
• [Presentation] Block Checker/Diagonal Transformation Matrices, Their Properties, and the Interplay with Fast-Lifting (2010)
  • Author(s): T.Hagiwara
  • Organizer: 計測自動制御学会 第10回制御部門大会
  • Place of Presentation: 熊本
  • Year and Date: 2010-03-16
• [Presentation] 離散時間非因果的周期時変スケーリングに基づくロバスト制御器設計手法の性質とその応用 (2009)
  • Author(s): 細江陽平, 萩原朋道
  • Organizer: 計測自動制御学会 第38回制御理論シンポジウム
  • Place of Presentation: 大阪
  • Year and Date: 2009-09-15
• [Presentation] On Numerical Computation of the Spectrum of a Class of Integral Operators via Non-causal Hold Discretization (2009)
  • Author(s): K.Hirata, A.Itokazu, T.Hagiwara
  • Organizer: 8^<th> IFAC Workshop on Time-Delay Systems
  • Place of Presentation: Sinaia, Romania
  • Year and Date: 2009-09-02
• [Presentation] Fast-Lifting Approach to the Computation of the Spec-trum of Retarded Time-Delay Systems (2009)
  • Author(s): T. Hagiwara and K. Hirata
  • Organizer: Eu-ropean Control Conference 2009
  • Place of Presentation: Budapest
  • Year and Date: 2009-08-24
• [Presentation] Fast-lifting Approach to the Computation of the Spectrum of Retarded Time-delay Systems (2009)
  • Author(s): T.Hagiwara, K.Hirata
  • Organizer: European Control Conference 2009
  • Place of Presentation: Budapest, Hungary
  • Year and Date: 2009-08-24
• [Presentation] Stability Analysis of Nonlinear Sampled-data Systems via Causal Linear Periodically Time-varying Scaling (2009)
  • Author(s): K.Morioka, T.Hagiwara
  • Organizer: ICROS-SICE International Joint Conference 2009
  • Place of Presentation: Fukuoka
  • Year and Date: 2009-08-19
• [Presentation] 補正型Fast-Sample/Fast-Hold近似によるH∞離散化の直達項の構造を利用した改善 (2009)
  • Author(s): 小堺祐平, 萩原朋道
  • Organizer: 第53回システム制御情報学会研究発表講演会
  • Place of Presentation: 神戸
  • Year and Date: 2009-05-21
• [Presentation] Quasi-finite-rank Approximation of Compression Operators in Sampled-data Systems and Time-delay Systems (2009)
  • Author(s): T.Hagiwara, K.Okada
  • Organizer: IFAC Workshop on Control Applications of Optimization
  • Place of Presentation: Jyvaskyla, Finland
  • Year and Date: 2009-05-06