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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2202.10397 |
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| _version_ | 1866910117341954048 |
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| author | Feng, Qian Zheng, Wei Xing Xiao, Feng Wang, Xiaoyu |
| author_facet | Feng, Qian Zheng, Wei Xing Xiao, Feng Wang, Xiaoyu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_10397 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dissipative Control of General Linear Time-Delay Systems: Applications of the Kronecker-Seuret Decomposition Feng, Qian Zheng, Wei Xing Xiao, Feng Wang, Xiaoyu Optimization and Control 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. |
| title | Dissipative Control of General Linear Time-Delay Systems: Applications of the Kronecker-Seuret Decomposition |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2202.10397 |