Kharitonov’s theorem and routh criterion for stability margin of interval systems

  • Yogesh V. HoteEmail author
  • J. R. P. Gupta
  • D. Roy Choudhury
Technical Notes and Correspondence


In this paper, it is shown that the gain margin and phase margin of interval system can be determined analytically using Kharitonov’s theorem and V. Krishnamurthi’s corollary on Routh criterion without using graphical and iterative techniques. Further, it is proved that the existing results of Anderson et al. [2] on the stability of low-order interval systems using Kharitonov’s theorem are only applicable for absolute stability of the interval system and it is not applicable for relative stability of the interval systems, i.e., for phase margin. The proposed technique and stability analysis for low-order interval systems are verified with examples.


Gain margin interval systems Kharitonov’s theoem phase margin routh criterion robust stability 


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Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yogesh V. Hote
    • 1
    Email author
  • J. R. P. Gupta
    • 1
  • D. Roy Choudhury
    • 2
  1. 1.Dept. of Instrumentation and Control EngineeringNSITNew DelhiIndia
  2. 2.I.P. UniversityDelhiIndia

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