Xu, Shengyuan; Lam, James; Huang, Shoudong; Yang, Chengwu \(H_\infty\) model reduction for linear time-delay systems: Continuous-time case. (English) Zbl 1022.93008 Int. J. Control 74, No. 11, 1062-1074 (2001). In the last decade the so-called \(H_\infty\) model reduction has received much attention becoming an important research topic in applied mathematics. Basically the reduction problem involves approximating a stable system with \(n\) states by another stable system with \(m< n\) states such that the associated model error satisfies a prescribed \(H_\infty\) norm bound constraint. Most of the results have been derived in the context of continuous and discrete-time systems without delays and parameter uncertainties. The main aim of the present paper consists in studying the problem of \(H_\infty\) model reduction for linear continuous time-delay systems. The case including systems with parameter uncertainties is analysed separately. In this respect, sufficient conditions based upon linear matrix inequalities and a coupling non-convex rank constraint are proposed in order to assure the existence of the desired reduced-order model. A simple illustrative example is also given to show the effectiveness of the proposed approach. Reviewer: Pablo Gonzalez-Vera (La Laguna) Cited in 44 Documents MSC: 93B11 System structure simplification 93C23 Control/observation systems governed by functional-differential equations 93B36 \(H^\infty\)-control 15A39 Linear inequalities of matrices Keywords:transfer function matrix; \(H_\infty\) model reduction; time-delay systems; parameter uncertainties; linear matrix inequalities; non-convex rank constraint PDFBibTeX XMLCite \textit{S. Xu} et al., Int. J. Control 74, No. 11, 1062--1074 (2001; Zbl 1022.93008) Full Text: DOI