View in EDS

Mathematical Approach for Robust Stability and for Robustly Strictly Positive Real on an Uncertain Plant Family of Complex Polynomials.

Saved in:
Bibliographic Details
Title: Mathematical Approach for Robust Stability and for Robustly Strictly Positive Real on an Uncertain Plant Family of Complex Polynomials.
Authors: Ghosh, Buddhadev1 (AUTHOR), Chakraborty, Gargi1 (AUTHOR) gargichakraborty.math@gmail.com
Source: International Journal of Robust & Nonlinear Control. 5/10/2026, Vol. 36 Issue 7, p4089-4105. 17p.
Subjects: Robust stability analysis, Hurwitz polynomials, Polynomials, Control theory (Engineering)
Abstract: In this article, we present a robust control problem for a family of uncertain interval plants 풫={P(s,q,r,u,v)=N(s,q,r)/D(s,u,v):q∈Q,r∈R,u∈U,v∈V}. We proposed a novel method introducing eight complex‐coefficient Kharitonov polynomials uniquely by minimizing and maximizing the concept of multilinear functions with four uncertain parameters. These polynomials define the vertices of a Kharitonov cuboid, which characterizes both robust stability and the robustly strictly positive real (SPR) property of the plant family. Thus, the introduction of this Kharitonov cuboid stands as a novel innovation in this article. The proposed approach offers two key contributions. Initially, we demonstrate the stability of the eight unique Kharitonov polynomials employing Hurwitz stability criteria, followed by the utilization of Kharitonov's theorem to ensure robust stability of 풫. Subsequently, we establish the robustly SPR property by ensuring that the minimum values of the real and imaginary parts of the plant's frequency response remain positive, and we also analyze the stability of the numerator and denominator of each interval plant (P$$ P $$). Numerical examples and simulations illustrate the effectiveness of the method, showing the motion of the Kharitonov cuboid and confirming the robust stability of the system. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Robust & Nonlinear Control is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 192765769
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Mathematical Approach for Robust Stability and for Robustly Strictly Positive Real on an Uncertain Plant Family of Complex Polynomials.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Ghosh%2C+Buddhadev%22">Ghosh, Buddhadev</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Chakraborty%2C+Gargi%22">Chakraborty, Gargi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> gargichakraborty.math@gmail.com</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Robust+%26+Nonlinear+Control%22">International Journal of Robust & Nonlinear Control</searchLink>. 5/10/2026, Vol. 36 Issue 7, p4089-4105. 17p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Robust+stability+analysis%22">Robust stability analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Hurwitz+polynomials%22">Hurwitz polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Control+theory+%28Engineering%29%22">Control theory (Engineering)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this article, we present a robust control problem for a family of uncertain interval plants 풫={P(s,q,r,u,v)=N(s,q,r)/D(s,u,v):q∈Q,r∈R,u∈U,v∈V}. We proposed a novel method introducing eight complex‐coefficient Kharitonov polynomials uniquely by minimizing and maximizing the concept of multilinear functions with four uncertain parameters. These polynomials define the vertices of a Kharitonov cuboid, which characterizes both robust stability and the robustly strictly positive real (SPR) property of the plant family. Thus, the introduction of this Kharitonov cuboid stands as a novel innovation in this article. The proposed approach offers two key contributions. Initially, we demonstrate the stability of the eight unique Kharitonov polynomials employing Hurwitz stability criteria, followed by the utilization of Kharitonov's theorem to ensure robust stability of 풫. Subsequently, we establish the robustly SPR property by ensuring that the minimum values of the real and imaginary parts of the plant's frequency response remain positive, and we also analyze the stability of the numerator and denominator of each interval plant (P$$ P $$). Numerical examples and simulations illustrate the effectiveness of the method, showing the motion of the Kharitonov cuboid and confirming the robust stability of the system. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Robust & Nonlinear Control is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=192765769
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1002/rnc.70403
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 17
        StartPage: 4089
    Subjects:
      – SubjectFull: Robust stability analysis
        Type: general
      – SubjectFull: Hurwitz polynomials
        Type: general
      – SubjectFull: Polynomials
        Type: general
      – SubjectFull: Control theory (Engineering)
        Type: general
    Titles:
      – TitleFull: Mathematical Approach for Robust Stability and for Robustly Strictly Positive Real on an Uncertain Plant Family of Complex Polynomials.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Ghosh, Buddhadev
      – PersonEntity:
          Name:
            NameFull: Chakraborty, Gargi
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 10
              M: 05
              Text: 5/10/2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 10498923
          Numbering:
            – Type: volume
              Value: 36
            – Type: issue
              Value: 7
          Titles:
            – TitleFull: International Journal of Robust & Nonlinear Control
              Type: main
ResultId 1