Disturbance Attenuation Regulator I-B: Signal Bound Convergence and Steady-State

[2601.10868] Disturbance Attenuation Regulator I-B: Signal Bound Convergence and Steady-State Skip to main content Search Submit Donate Log in Electrical Engineering and Systems Science > Systems and Control arXiv:2601.10868 (eess) [Submitted on 15 Jan 2026 ( v1 ), last revised 24 Aug 2026 (this version, v3)] Title: Disturbance Attenuation Regulator I-B: Signal Bound Convergence and Steady-State Authors: Davide Mannini , James B. Rawlings View PDF HTML (experimental) Abstract: This paper establishes convergence and steady-state properties for the signal bound disturbance attenuation regulator (SiDAR). Building on the finite horizon recursive solution developed in a companion paper, we introduce the steady-state SiDAR and derive its tractable linear matrix inequality (LMI) with $O(n^3)$ complexity. Systems are classified as degenerate or nondegenerate based on steady-state solution properties. For nondegenerate systems, the finite horizon solution converges to the steady-state solution for all states as the horizon approaches infinity. For degenerate systems, convergence holds in one region of the state space, while a turnpike arises in the complementary region. When convergence holds, the optimal multiplier and control gain are obtained directly from the LMI solution. Numerical examples illustrate convergence behavior and turnpike phenomena. Companion papers address the finite horizon SiDAR solution and the stage bound disturbance attenuation regulator (StDAR). Subjects: Systems and Control (eess.SY) Cite as: arXiv:2601.10868 [eess.SY] (or arXiv:2601.10868v3 [eess.SY] for this version) https://doi.org/10.48550/arXiv.2601.10868 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Davide Mannini [ view email ] [v1] Thu, 15 Jan 2026 21:39:09 UTC (750 KB) [v2] Thu, 21 May 2026 17:18:31 UTC (752 KB) [v3] Mon, 24 Aug 2026 18:04:01 UTC (753 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: eess.SY < prev | next > new | recent | 2026-01 Change to browse by: cs cs.SY eess References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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