[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84172-en":3,"doc-seo-84172-105":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},84172,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Observer-Based Target Control for Mismatched Time-Delay Systems","Observer-based target control is studied for linear time-delay systems under simultaneous mismatched delays in input, state, and output channels. Instead of conservative full-state regulation, the objective is to asymptotically stabilize a specified linear target output z_o(t)=F_o x(t) despite asymmetric dual-channel latency effects. A reduced-order modeling framework projects the high-dimensional dynamics onto the row space of F_o, yielding a lower-dimensional target subspace. Based on this projection, an observer-based control scheme is developed to achieve precise target stabilization while addressing delayed measurements and unavailable target variables.","Observer-Based Target Control for Mismatched  \nTime-Delay Systems  \nHieu Trinh  \narXiv :2607 .07036v1 [ ee ss . SY] 8 Jul 2026  \nAbstract—This paper addresses observer-based target control for linear time-delay systems subject to simultaneous, mismatched input and output latencies. While full-state regulation is often conservative and computationally intensive, practical engineering objectives typically require controlling only specific linear combinations of states, or target outputs. To overcome the challenges posed by these asymmetric, dual-channel delays, we propose a reduced-order modeling framework inspired by the structural philosophy of Fernando and Darouach [1]. By projecting the high-dimensional plant dynamics onto the row space of the target output matrix Fo, the controller focuses strictly on the lower-dimensional target subspace. Based on this projection, an observer-based control scheme is developed to ensure precise target stabilization despite the simultaneous, mismatched input, state, and output latencies.  \nIndex Terms—Time-delay compensators, delayed measurements, input delays, functional observers, target output controllers.  \nI. SYSTEM DESCRIPTION AND PROBLEM STATEMENT Consider the following time-delay system:  \nx˙(t) = Ax(t) + Ad x (t − τx ) + Bu(t − τu), (1)  \ny (t) = Cx (t − τy), (2)  \nwhere x (t) ∈ Rn is the state vector, u (t) ∈ Rr is the control input vector, and y(t) ∈ Rp is the measured output vector. The constants τx > 0, τu > 0 and τy > 0 represent the time delaysin the state, control input, and output channels, respectively. The initial condition is defined by the function x (t) = ρ (t) for t ∈ [−τmax , 0], where τmax = max{τx ,τy } . The system matrices A, Ad ∈ Rn ×n , B ∈ Rn ×r , and C ∈ Rp ×n are constant. Without loss of generality, it is assumed that B has full column rank and C has full row rank. We do not assume that A is a Hurwitz matrix. In fact, even if A is Hurwitz, the overall system (1) may still be destabilized by the presence of the delayed term Adx (t − τx) .  \nThe target output vector to be regulated is defined as:  \nzo (t) = Fox (t), (3)  \nwhere zo (t) ∈ Rm and Fo ∈ Rm ×n is a constant matrix. We assume Fo has full row rank (m \u003C n) because the linear functions targeted for control are linearly independent; ensuring the regulation of these independent components inherently guarantees the control of any linearly dependent variations.  \nThe primary objective of this paper is to design an observerbased controller that asymptotically drives the target output  \nHieu Trinh is with the School of Engineering, Deakin University, Waurn Ponds, 75 Pigdons Road, Geelong, Australia. (email: [hieu.trinh@deakin.edu.au](hieu.trinh@deakin.edu.au))  \nvector to the origin, i.e., limt→∞ zo (t) = 0, from any initial condition.  \nA key contribution of this work is the development of a reduced-order observer-based design, achieved by projecting the full state dynamics directly onto the row space of the target output matrix Fo [1] . While traditional approaches burden the observer with reconstructing the entire high-dimensional state vector x (t), the proposed projection method strategically isolates the lower-dimensional subspace that actively dictates the target tracking profile. Specifically, to stabilize the target output under severe latencies, we introduce a delaycompensated control strategy that regulates the linear combination Fox (t) rather than the full state vector. As noted in [1], the asymptotic stability of the target output does not inherently require the asymptotic stability of the entire state vector x(t) . This distinction highlights the practical advantage of targeting a specific subspace, avoiding the unnecessary conservative constraints of full-state stabilization.  \nTo handle the time delay in the input channel effectively and render the synthesis problem tractable, we consider the case where τx > τu (the case where τu > τx is discussed in Remark 2) . The proposed control law is structur","cbCaiqYqkB9ttC37","https://ap.wps.com/l/cbCaiqYqkB9ttC37","pdf",224879,1,9,"English","en",105,"# System Description and Problem Statement\n## Objective and System Setup\n## Target Output Definition and Assumptions\n# Reduced-Order Observer-Based Control Design\n## Projection onto Target Output Row Space\n## Delay-Compensated Control Law and Implementation\n# Functional Observer Architecture\n## Estimation of Delayed Control Terms","[{\"question\":\"What problem does the paper address in time-delay systems?\",\"answer\":\"It addresses observer-based target control for linear time-delay systems where input and output (and related state) delays are simultaneous but mismatched across channels.\"},{\"question\":\"Why is the method reduced-order instead of full-state regulation?\",\"answer\":\"The approach targets specific linear combinations of states (target outputs) rather than regulating the entire state, avoiding conservative and computationally intensive full-state stabilization requirements.\"},{\"question\":\"How does the controller ensure stabilization of the target output under delays?\",\"answer\":\"It uses a delay-compensated control law that regulates z_o(t)=F_o x(t), while a functional observer estimates the delayed feedback quantities so the designed control can be implemented despite delayed measurements.\"}]",1784193635,23,{"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},"observer-based-target-control-for-mismatched-time-delay-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/observer-based-target-control-for-mismatched-time-delay-systems/84172/",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 time-delay systems?","Question",{"text":75,"@type":76},"It addresses observer-based target control for linear time-delay systems where input and output (and related state) delays are simultaneous but mismatched across channels.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is the method reduced-order instead of full-state regulation?",{"text":80,"@type":76},"The approach targets specific linear combinations of states (target outputs) rather than regulating the entire state, avoiding conservative and computationally intensive full-state stabilization requirements.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the controller ensure stabilization of the target output under delays?",{"text":84,"@type":76},"It uses a delay-compensated control law that regulates z_o(t)=F_o x(t), while a functional observer estimates the delayed feedback quantities so the designed control can be implemented despite delayed 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