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Frequency-domain criterion on the stabilizability for infinite-dimensional linear control systems

Karl Kunisch, Gengsheng Wang, Huaiqiang Yu

Abstract

A quantitative frequency-domain condition related to the exponential stabilizability for infinite-dimensional linear control systems is presented. It is proven that this condition is necessary and sufficient for the stabilizability of special systems, while it is a necessary condition for the stabilizability in general. Applications are provided.

Frequency-domain criterion on the stabilizability for infinite-dimensional linear control systems

Abstract

A quantitative frequency-domain condition related to the exponential stabilizability for infinite-dimensional linear control systems is presented. It is proven that this condition is necessary and sufficient for the stabilizability of special systems, while it is a necessary condition for the stabilizability in general. Applications are provided.
Paper Structure (15 sections, 15 theorems, 169 equations)

This paper contains 15 sections, 15 theorems, 169 equations.

Table of Contents

  1. Introduction
  2. Notation
  3. Control problem
  4. Motivation and novelty
  5. Main results
  6. Related works
  7. Plan of this paper
  8. Other criteria on the stabilization
  9. Proofs of the main theorems
  10. Applications
  11. Ginzburg--Landau equation in $\mathbb{R}^N$
  12. Fractional heat equation in $\mathbb{R}^N$
  13. One-dimensional heat equation with point-wise controls
  14. Heat equation with time delay in $\mathbb{R}^N$
  15. Appendix

Key Result

Lemma 1.5

Theorems & Definitions (42)

  • Remark 1.1
  • Definition 1.2
  • Definition 1.3
  • Remark 1.4
  • Lemma 1.5
  • Remark 1.6
  • Lemma 1.7
  • Definition 1.8
  • Remark 1.9
  • Theorem 1.10
  • ...and 32 more