[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82246-en":3,"doc-seo-82246-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82246,962075114765,"Quinn","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Cyclic Reformulation-Based Identification and Polytopic Uncertainty Modeling for Multirate Systems","Modern control systems use heterogeneous sensors operating at different sampling rates, where intermittently missing outputs complicate system identification. This paper presents a non-iterative, control-oriented method for multirate systems using cyclic reformulation: multirate data are converted into an expanded time-invariant form, producing M parameter sets from one dataset. The centroid yields a noise-reduced nominal model, while the convex hull provides a polytopic uncertainty model for vertex-based robust LMI design. Simulations show improved validation FIT for both SISO and MIMO cases.","arXiv :2607 .09194v1 [ ee ss . SY] 10 Jul 2026  \nCyclic Reformulation-Based Identification and Polytopic Uncertainty Modeling for Multirate  \nSystems ∗  \nHiroshi Okajima, Kakeru Ono  \nFaculty of Advanced Science and Technology, Kumamoto University, Japan  \nKeywords: Multirate Systems; System Identification; Cyclic Reformulation; Centroid Model; Polytopic Uncertainty; Sensor Fusion.  \nAbstract  \nModern control systems increasingly rely on heterogeneous sensors operating at different sampling rates, where intermittently missing outputs pose fundamental challenges for system identification. This paper proposes a non-iterative, control-oriented identification method for multirate systems based on cyclic reformulation. The method transforms multirate data into an expanded time-invariant representation and yields M parameter sets from a single input-output dataset, where M is the least common multiple of the sensor sampling periods. These parameter sets are used in two complementary ways: their centroid serves as a noise-reduced nominal model, while their convex hull gives apolytopic uncertainty model compatible with vertex-based LMI robust control design. Building on the noise-free structural recovery theorem of the authors’ preceding work, which is restated here in the notation of the present paper, the present paper newly introduces the centroid and polytopic models derived from the M parameter sets; finite-noise behavior is treated as an empirical observation and is evaluated numerically. Numerical simulations support both models: an illustrative SISO example shows that the centroid attains higher validation FIT than the best individual vertex and substantially outperforms an interpolation-based baseline, while a MIMO multirate sensing example confirms, in line with the LTI counterpart, that the constructed polytope contains models whose validation FIT exceeds 95% on average even at the highest tested noise level. The polytope is interpreted cautiously, with finite-noise behavior assessed through output-level validation statistics rather than realization-dependent matrix-coordinate distances. The proposed framework therefore links multirate system identification with robust-control-oriented uncertainty modeling without iterative EM-type optimization.  \n∗ Corresponding author: H. Okajima. Email: [okajima@cs.kumamoto-u.ac.jp](okajima@cs.kumamoto-u.ac.jp)  \n1 Introduction  \nSystem identification plays a crucial role in model-based control design, where accurate mathematical models directly determine control performance [1, 2, 3, 4] . Recent advances have extended identification techniques to nonlinear systems [5], periodic systems [6, 7], and various practical applications.  \nIn modern control systems, feedback control using multiple sensors is common. When these sensors are based on different physical principles, they often operate at different sampling rates, as each sensing principle has its own achievable rate under hardware and communication constraints. Such multirate sensing environments arise frequently in mobile robot control [8, 9] and sampled-data control systems [10] . Since multirate systems can be viewed as systems with periodically unavailable output measurements, their identification is significantly more challenging than that of standard linear time-invariant systems.  \nSeveral approaches have been proposed for multirate system identification. Subspace-based identification for non-uniformly sampled multirate data was developed in [11], and Kalman filter design for fault detection in such systems was addressed in [12] . Lifting techniques [13, 14] enable fastrate model identification but face difficulties in recovering original system parameters due to variable products in the expanded state space. Modified subspace methods for periodically non-uniformly sampled systems were also proposed in [15] . Stochastic gradient approaches offer another direction: partially coupled algorithms for non-uniformly sampled systems were developed in [16],","cbCaiuLcAiCzCxuM","https://ap.wps.com/l/cbCaiuLcAiCzCxuM","pdf",361553,1,32,"English","en",105,"# Introduction\n## Multirate sensing and identification challenges\n## Related approaches (subspace, lifting, stochastic gradient)\n## EM and maximum-likelihood iterative methods\n## Cyclic reformulation for periodically time-varying and multirate systems","[{\"question\":\"What problem does the paper address in multirate system identification?\",\"answer\":\"It addresses identification when multiple sensors operate at different sampling rates and outputs are intermittently missing, making multirate identification harder than standard LTI cases.\"},{\"question\":\"How does cyclic reformulation enable non-iterative identification here?\",\"answer\":\"The method transforms multirate data into an expanded time-invariant representation and yields M parameter sets from a single input-output dataset, where M is the least common multiple of sampling periods.\"},{\"question\":\"How are the obtained parameter sets used for control-oriented uncertainty modeling?\",\"answer\":\"Their centroid is used as a noise-reduced nominal model, and their convex hull forms a polytopic uncertainty model compatible with vertex-based robust LMI control design.\"}]",1784179129,81,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"cyclic-reformulation-based-identification-and-polytopic-uncertainty-modeling-for-multirate-systems","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/cyclic-reformulation-based-identification-and-polytopic-uncertainty-modeling-for-multirate-systems/82246/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the paper address in multirate system identification?","Question",{"text":75,"@type":76},"It addresses identification when multiple sensors operate at different sampling rates and outputs are intermittently missing, making multirate identification harder than standard LTI cases.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does cyclic reformulation enable non-iterative identification here?",{"text":80,"@type":76},"The method transforms multirate data into an expanded time-invariant representation and yields M parameter sets from a single input-output dataset, where M is the least common multiple of sampling periods.",{"name":82,"@type":73,"acceptedAnswer":83},"How are the obtained parameter sets used for control-oriented uncertainty modeling?",{"text":84,"@type":76},"Their centroid is used as a noise-reduced nominal model, and their convex hull forms a polytopic uncertainty model compatible with vertex-based robust LMI control 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