Dissipative Control of General Linear Time-Delay Systems: Applications of the Kronecker-Seuret Decomposition

[2202.10397] Dissipative Control of General Linear Time-Delay Systems: Applications of the Kronecker-Seuret Decomposition Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2202.10397 (math) [Submitted on 21 Feb 2022 ( v1 ), last revised 9 Apr 2026 (this version, v12)] Title: Dissipative Control of General Linear Time-Delay Systems: Applications of the Kronecker-Seuret Decomposition Authors: Qian Feng , Wei Xing Zheng , Feng Xiao , Xiaoyu Wang View a PDF of the paper titled Dissipative Control of General Linear Time-Delay Systems: Applications of the Kronecker-Seuret Decomposition, by Qian Feng and Wei Xing Zheng and Feng Xiao and Xiaoyu Wang View PDF Abstract: Stabilizing autonomous linear time delay systems, particularly when addressing an unlimited number of pointwise and distributed delays (DDs) under dissipative constraints, poses a significant challenge. Existing solutions are often hindered by theoretical limitations, numerical obstacles, or an inability to address the complexities of the delay integral kernels. In this paper, we propose a unified framework to tackle the above problem by employing the concept of the Kronecker-Seuret decomposition (KSD) for matrix-valued functions, which we recently have developed for the analysis of complex delay structures in coordination with the Krasovski\uı functional approach. Our strategy can simultaneously address two distinct control problems, where the matrix kernels of DDs can contain an unlimited number of square-integrable functions. We show in detail how the KSD can factorize and approximate different kernel functions simultaneously without introducing conservatism. Furthermore, the use of KSD also enables us to construct complete-type functionals, whose integral kernels can include any number of weakly differentiable and linearly independent functions, underpinned by the utilization of novel integral inequalities derived from the least-squares principle. The solution to each synthesis problem comprises two theorems accompanied by an iterative algorithm, which can be utilized as a single package to compute controller gains, thus eliminating the need for nonlinear solvers. We present the testing results of two challenging examples, which could not be addressed by existing methods, to demonstrate the effectiveness of our methodology. Additionally, the paper reviews recent advancements in the research of time-delay systems, providing a valuable reference for both emerging and established researchers. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2202.10397 [math.OC] (or arXiv:2202.10397v12 [math.OC] for this version) https://doi.org/10.48550/arXiv.2202.10397 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Qian Feng [ view email ] [v1] Mon, 21 Feb 2022 17:51:10 UTC (1,182 KB) [v2] Wed, 6 Apr 2022 09:18:24 UTC (813 KB) [v3] Mon, 18 Apr 2022 16:16:27 UTC (819 KB) [v4] Thu, 1 Jun 2023 04:19:12 UTC (816 KB) [v5] Tue, 6 Jun 2023 11:49:13 UTC (816 KB) [v6] Tue, 20 Jun 2023 16:30:43 UTC (831 KB) [v7] Sat, 24 Jun 2023 14:46:45 UTC (831 KB) [v8] Sun, 6 Aug 2023 19:59:28 UTC (860 KB) [v9] Wed, 23 Aug 2023 03:00:47 UTC (932 KB) [v10] Wed, 7 Aug 2024 14:15:21 UTC (797 KB) [v11] Thu, 14 Nov 2024 11:40:06 UTC (727 KB) [v12] Thu, 9 Apr 2026 19:48:18 UTC (724 KB) Full-text links: Access Paper: View a PDF of the paper titled Dissipative Control of General Linear Time-Delay Systems: Applications of the Kronecker-Seuret Decomposition, by Qian Feng and Wei Xing Zheng and Feng Xiao and Xiaoyu Wang View PDF view license Current browse context: math.OC < prev | next > new | recent | 2022-02 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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