Robust Control of General Linear Delay Systems under Dissipativity: Part I -- A KSD-based Framework

Fuente: arXiv
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Main Authors: Feng, Qian, Zheng, Wei Xing, Wang, Xiaoyu, Xiao, Feng
Format: Preprint
Published: 2025
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author Feng, Qian
Zheng, Wei Xing
Wang, Xiaoyu
Xiao, Feng
author_facet Feng, Qian
Zheng, Wei Xing
Wang, Xiaoyu
Xiao, Feng
contents This paper introduces an effective framework for designing memoryless dissipative full-state feedback for general linear delay systems via the Krasovskiĭ functional (KF) approach, where an arbitrary finite number of pointwise and general distributed delays (DDs) exists in the state, input and output. To handle the infinite dimensionality of DDs, we employ the Kronecker-Seuret Decomposition (KSD) which we recently proposed for analyzing matrix-valued functions in the context of delay systems. The KSD enables factorization or least-squares approximation of any number of $\fL^2$ DD kernels from any number of DDs without introducing conservatism. This also facilitates the construction of a complete-type KF with flexible integral kernels by means of a novel integral inequality derived from the least-squares principle. Our solution includes two theorems and an iterative algorithm to compute controller gains without relying on nonlinear solvers. A numerical example is tested to show the effectiveness of the proposed approach.
format Preprint
id arxiv_https___arxiv_org_abs_2504_00165
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Robust Control of General Linear Delay Systems under Dissipativity: Part I -- A KSD-based Framework
Feng, Qian
Zheng, Wei Xing
Wang, Xiaoyu
Xiao, Feng
Optimization and Control
Systems and Control
This paper introduces an effective framework for designing memoryless dissipative full-state feedback for general linear delay systems via the Krasovskiĭ functional (KF) approach, where an arbitrary finite number of pointwise and general distributed delays (DDs) exists in the state, input and output. To handle the infinite dimensionality of DDs, we employ the Kronecker-Seuret Decomposition (KSD) which we recently proposed for analyzing matrix-valued functions in the context of delay systems. The KSD enables factorization or least-squares approximation of any number of $\fL^2$ DD kernels from any number of DDs without introducing conservatism. This also facilitates the construction of a complete-type KF with flexible integral kernels by means of a novel integral inequality derived from the least-squares principle. Our solution includes two theorems and an iterative algorithm to compute controller gains without relying on nonlinear solvers. A numerical example is tested to show the effectiveness of the proposed approach.
title Robust Control of General Linear Delay Systems under Dissipativity: Part I -- A KSD-based Framework
topic Optimization and Control
Systems and Control
url https://arxiv.org/abs/2504.00165