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Stability criteria of linear delay differential systems based on fundamental matrix

Guang-Da Hu

Abstract

We investigate stability of linear delay differential systems. Stability criteria of the systems are derived based on integrals of the fundamental matrix. They are necessary and sufficient conditions for delay-dependent stability of the systems. Numerical examples are given to illustrate the main results.

Stability criteria of linear delay differential systems based on fundamental matrix

Abstract

We investigate stability of linear delay differential systems. Stability criteria of the systems are derived based on integrals of the fundamental matrix. They are necessary and sufficient conditions for delay-dependent stability of the systems. Numerical examples are given to illustrate the main results.

Paper Structure

This paper contains 6 sections, 5 theorems, 61 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Stability Criteria
  4. Numerical Examples
  5. Conclusions
  6. Acknowledgements

Key Result

Lemma 2.1

(GySab) If system (eq:dde) is asymptotically stable, then the matrix $(A_{0}+\sum_{j=1}^{m}A_{j})$ is invertible and

Figures (2)

  • Figure 1: $||X(t)||_{F}$: Frobenius Norm of Fundamental Matrix $X(t)$
  • Figure 2: $||X(t)||_{F}$: Frobenius Norm of Fundamental Matrix $X(t)$

Theorems & Definitions (11)

  • Lemma 2.1
  • Lemma 2.2
  • Theorem 3.1
  • Remark 3.1
  • Remark 3.2
  • Theorem 3.2
  • Remark 3.3
  • Theorem 3.3
  • Remark 3.4
  • Example 4.1
  • ...and 1 more