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This chapter covers the framework of PSD-based eigenvalue computation theory for time-delay systems, which consists of mapping, discretization, transform, estimation, and correction. The basic idea is that, the spectra of a time-delay system can be mapped to those of the infinite-dimensional semigroup operators; then eigenvalues of the finite-dimensional discretized matrices approximating semigroup operators are in turn used as the estimated eigenvalues of the time-delay system.

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PSD-Based Eigenvalue Computation Framework for Large-Scale Time-Delay Systems

  • 章节

  • 发表日期：

    2025年

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  • Hua Ye,
  • Yutian Liu,
  • Xiaofan Jia

摘要

This chapter covers the framework of PSD-based eigenvalue computation theory for time-delay systems, which consists of mapping, discretization, transform, estimation, and correction. The basic idea is that, the spectra of a time-delay system can be mapped to those of the infinite-dimensional semigroup operators; then eigenvalues of the finite-dimensional discretized matrices approximating semigroup operators are in turn used as the estimated eigenvalues of the time-delay system.