Kharitonov’s theorem and routh criterion for stability margin of interval systems
- 374 Downloads
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.  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.
KeywordsGain margin interval systems Kharitonov’s theoem phase margin routh criterion robust stability
Unable to display preview. Download preview PDF.
- R. E. Precup and S. Preitl, “PI and PID controllers tuning for integral-type servo systems to ensure robust stability and controller robustness,” Springer Journal on Electrical Engineering, vol. 88, pp.149–156, 2006.Google Scholar
- D. R. Choudhury, Modern Control Engineering, Prentice Hall India, 2005.Google Scholar
- V. Krishnamurthy, W. K. Sa’id, and N. A. Al-Awad, “Phase margin of linear time invariant systems from Routh array,” IEE Proceedings-D, vol. 138, no. 4, pp. 410–412, 1991.Google Scholar
- M. B. Argoun and M M. Bayoumi, “Robust gain and phase margin for interval uncertain systems,” Proc. of Canadian Conf. on Electrical and Computer Engg., pp. 73–78, 1993.Google Scholar
- F. R. Gantmacher, The Theory of Matrices, vol. II., Ch. 15, Chelsea, New York, 1964.Google Scholar
- R. C. Dorf and R. H. Bishop, Modern Control Engineering, Eighth Edition, Addison Wesley, 1999.Google Scholar
- M. Gopal, Control Systems (Principles and Design), Tata McGraw Hill, 2008.Google Scholar
- J. Ackerman, Robust Control: Systems with Uncertain Physical Parameters, Springer-Verlag, 1993.Google Scholar