New double integral inequality with application to stability analysis for linear retarded systems

Rupak Datta, Rajeeb Dey, Baby Bhattacharya, Ramasamy Saravanakumar, Choon Ki Ahn

Research output: Contribution to journalArticle

Abstract

This paper presents the development of a new double integral inequality (II) with the motivation of yielding quadratic approximation. It is well known that approximating integral quadratic terms with quadratic terms involves a certain degree of conservatism. In this paper, a sufficient gap has been identified in the approximation of two recent IIs reported in the literature, thereby leading to the new double II. The developed inequality has been applied to access the stability of a linear retarded system to estimate a maximum delay upper-bound. Furthermore, a mathematical relationship of the new double II with existing inequalities is discussed to show that the developed inequality is more general, effective and bears less computational burden. Four numerical examples are given to validate the authors' claim with regard to the effective estimate of delay bound results for a linear retarded system.

Original languageEnglish
Pages (from-to)1500-1513
Number of pages14
JournalIET Control Theory and Applications
Volume13
Issue number10
DOIs
Publication statusPublished - 2019 Jul 2

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Double integral
Integral Inequality
Linear systems
Stability Analysis
Quadratic Approximation
Term
Estimate
Sufficient
Upper bound
Numerical Examples
Approximation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Human-Computer Interaction
  • Computer Science Applications
  • Control and Optimization
  • Electrical and Electronic Engineering

Cite this

New double integral inequality with application to stability analysis for linear retarded systems. / Datta, Rupak; Dey, Rajeeb; Bhattacharya, Baby; Saravanakumar, Ramasamy; Ahn, Choon Ki.

In: IET Control Theory and Applications, Vol. 13, No. 10, 02.07.2019, p. 1500-1513.

Research output: Contribution to journalArticle

Datta, Rupak ; Dey, Rajeeb ; Bhattacharya, Baby ; Saravanakumar, Ramasamy ; Ahn, Choon Ki. / New double integral inequality with application to stability analysis for linear retarded systems. In: IET Control Theory and Applications. 2019 ; Vol. 13, No. 10. pp. 1500-1513.
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