Skip to main content
Log in

An Improved Approach for Stability Analysis of Discrete System

  • Published:
Journal of Control, Automation and Electrical Systems Aims and scope Submit manuscript

Abstract

This paper presents an improved technique to analyze the stability margin of the discrete systems. The presented approach is based on the reduced conservatism of eigenvalues and scaling of Gerschgorin circles. The mathematical proof and sufficient condition with suitable scaling is stated for the conservatism of eigenvalues. Moreover, the presented technique is demonstrated with the numerical examples. Further, the improved results are compared with the existing methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  • Boese, F. G., & Luther, W. J. (1989). A note on a classical bound for the moduli of all zeros of a polynomial. IEEE Transaction on Automatic Control, 34(9), 998–1001.

    Article  MathSciNet  MATH  Google Scholar 

  • Choudhury, D. R. (1973). Algorithm for power of companion matrix and its application. IEEE Transaction on Automatic Control, 18(2), 179–180.

    Article  Google Scholar 

  • Choudhury, D. R. (2005). Modern control engineering. New Delhi: Prentice Hall of India.

    Google Scholar 

  • Dey, A., & Kar, Harnath. (2012). An LMI based criterion for the global asymptotic stability of 2-D discrete state-delayed systems with saturation nonlinearities. Digital Signal Processing, 22(4), 633–639.

    Article  MathSciNet  Google Scholar 

  • Gaidhane, V. H., & Hote, Y. V. (2016). A new approach for stability analysis of discrete systems. IETE Technical Review, 33(5), 466–471.

    Article  Google Scholar 

  • Gaidhane, V. H., Hote, Y. V., & Singh, V. (2014). An efficient approach for face recognition based on common eigenvalues. Pattern Recognition, 47(5), 1869–1879.

    Article  Google Scholar 

  • Gaidhane, V. H., Hote, Y. V., & Singh, V. (2015). Image focus measure based on polynomial coefficients and spectral radius. Signal, Image and Video Processing, 9(1), 203–211.

    Article  Google Scholar 

  • Gao, H., & Li, X. (2011). H filtering for discrete-time state-delayed systems with finite frequency specifications. IEEE Transaction on Automatic Control, 56(12), 2935–2941.

    Article  MathSciNet  MATH  Google Scholar 

  • Gerschgorin, S. (1931). Ueber die abgrenzung der eigenwerte einer matrix. Izv. Akad. Nauk. SSSR Ser Mat., 1(6), 749–754.

    Google Scholar 

  • Hasan, M.A., (2004). Inequalities and bounds for the zeros of polynomials using Perron-Frobenius and Gerschgorin theories. American control conference. Boston, Massachusetts, pp. 179–180.

  • Hote, Y. V., Choudhury, D. R., & Gupta, J. R. P. (2009). Robust stability analysis of the PWM push-pull DC–DC converter. IEEE Transaction on Power Electronics, 24(10), 2353–2356.

    Article  Google Scholar 

  • Hote, Y. V., Gupta, J. R. P., & Choudhury, D. R. (2011). A simple approach for stability margin of discrete system. Journal of Control Theory and Applications, 9(4), 567–570.

    Article  MathSciNet  Google Scholar 

  • Juang, Y.-T. (1989). Reduced conservatism of eigenvalue estimation. IEEE Transaction on Automatic Control, 34(9), 992–994.

    Article  MathSciNet  MATH  Google Scholar 

  • Koenings, T., Krueger, M., Luo, H., & Ding, S. X. (2018). A data-driven computation method for the gap metric and the optimal stability margin. IEEE Transactions on Automatic Control, 63(3), 805–810.

    Article  MathSciNet  MATH  Google Scholar 

  • Li, X., & Gao, H. (2011). A new model transformation of discrete-time systems with time-varying delay and its application to stability analysis. IEEE Transaction on Automatic Control, 56(9), 2172–2178.

    Article  MathSciNet  MATH  Google Scholar 

  • Li, X., Gao, H., & Gu, K. (2016). Delay-independent stability analysis of linear time-delay systems based on frequency discretization. Automatica, 70, 288–294.

    Article  MathSciNet  MATH  Google Scholar 

  • Lu, W.-S. (1998). Design of recursive digital filters with prescribed stability margin: A parameterization approach. IEEE Transaction on Circuits and Systems II: Analog and Digital Signal Processing, 40(9), 1289–1298.

    Google Scholar 

  • Meng, X., & Chen, T. (2014). Event triggered robust filter design for discrete-time systems. IET Control Theory and Applications, 8(2), 104–113.

    Article  MathSciNet  MATH  Google Scholar 

  • Phillips, C. L., & Nagle, H. T. (2007). Digital control system analysis and design. Upper Saddle River: Prentice Hall Press.

    MATH  Google Scholar 

  • Ramesh, P., & Vasudevan, K. (2018). Multidimensional linear discrete system stability analysis using single square matrix. In A. Garg, A. Bhoi, P. Sanjeevikumar & K. Kamani (Eds.), Advances in power systems and energy management. Lecture notes in electrical engineering (Vol. 436, pp. 499–509). Singapore: Springer.

    Chapter  Google Scholar 

  • Ratchagit, M. (2012). LMI approach to stability of discrete time-delay systems. International Journal of Pure and Applied Mathematics, 76(1), 69–78.

    MathSciNet  MATH  Google Scholar 

  • Yang, Z., & Xu, D. (2007). Stability analysis and design of impulsive control systems with time delay. IEEE Transaction on Automatic Control, 52(8), 1448–1454.

    Article  MathSciNet  MATH  Google Scholar 

  • Zeheb, E. (1991). On the largest modulus of polynomial zeros. IEEE Transaction on Circuits and Systems, 38(3), 333–337.

    Article  MATH  Google Scholar 

  • Zilovic, M. S., Roytman, L. M., Combettes, P. L., & Swamy, M. N. S. (1992). A bound for the zeros of polynomials. IEEE Transaction on Circuits and Systems I: Fundamentals Theory and Applications, 39(6), 476–478.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vilas H. Gaidhane.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gaidhane, V.H., Hote, Y.V. An Improved Approach for Stability Analysis of Discrete System. J Control Autom Electr Syst 29, 535–540 (2018). https://doi.org/10.1007/s40313-018-0396-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40313-018-0396-5

Keywords

Navigation