DOI QR코드

DOI QR Code

양자화와 오버플로우 비선형성을 가지는 이산시간 폴리토픽 불확실 지연 시스템의 강인 안정성

Robust Stability for Discrete-time Polytopic Uncertain Delay Systems with Quantization/overflow Nonlinearities

  • 김종해 (선문대학교 전자공학과)
  • Kim, Jong-Hae (Department of Electronic Eng., Sun Moon University)
  • 투고 : 2012.08.06
  • 심사 : 2012.11.12
  • 발행 : 2012.12.01

초록

In this paper, we consider the delay-dependent robust stability condition for polytopic uncertain systems with interval time-varying delay using various combinations of quantization and overflow nonlinearities. A robust stability condition for uncertain systems with time-varying delay and quantization/overflow nonlinearities is proposed by LMI(linear matrix inequality) and Lyapunov technique. It is shown that the proposed method is less conservative compared to the recent results by numerical examples.

키워드

참고문헌

  1. H. Kar and V. Singh, "Stability analysis of 1-D and 2-D fixed-point state -space digital filters using any combunation of overflow and quantization nonlinearities," IEEE Trans. on Signal Processing, vol. 49, no. 5, pp. 1097-1105, 2001. https://doi.org/10.1109/78.917812
  2. V. Singh, "Stability analysis of discrete-time systems in a state-space realisation with state saturation nonlinearities: linear matrix inequlaity approach," IEE Proc. Control Theory & Applications, vol. 152, pp. 9-12, 2005. https://doi.org/10.1049/ip-cta:20041118
  3. H. Kar, "A novel criterion for the global asymptotic stability of 2-D discrete systems described by Roesser model using saturation arithmetic," Digital signal Processing, vol. 20, pp. 1505-1510, 2010. https://doi.org/10.1016/j.dsp.2010.02.008
  4. L. J. Leclerc and P. H. Bauer, "New criteria for asymptotic stability of one- and multi dimensional state-space digital filters in fixed-point arithemetic," IEEE Trans. on Signal Processing, vol. 42, no. 1, pp. 46-53, 1994. https://doi.org/10.1109/78.258120
  5. H. Kar and V. Singh, "Robust stability of 2-D discrete systems described by the Fornasini-Marchesini second model employing quantization/overflow nonlinearities," IEEE Trans. on Circuits and Systems II, vol. 51, no. 11, pp. 598-602, 2004. https://doi.org/10.1109/TCSII.2004.836880
  6. V. K. R. Kandanvli and H. Kar, "Robust stabilityof discrete-time state-delayed systems with saturation nonlinearities: linear matrix inequality approach," Signal Processing, vol. 89, pp. 161-173, 2009. https://doi.org/10.1016/j.sigpro.2008.07.020
  7. V. K. R. Kandanvli and H. Kar, "An LMI condition for robust stability of discrete-time state-delayed systems using quantization/overflow nonlinearities," Signal Processing, vol. 89, pp. 2091-2102, 2009.
  8. V. K. R. Kandanvli and H. Kar, "Delay-dependent LMI condition for global asymptotic stability of discrete-time uncertain state-delayed systems using quantization/overflow nonlinearities," International Journal of Robust & Nonlinear Control, vol. 21, pp. 1611-1622, 2011. https://doi.org/10.1002/rnc.1654
  9. M. S. Mahmoud, Robust Control and Filtering for Time-delay Systems, New York, Marcel Dekker, Inc., 2000.
  10. S. Ma, C. Zhang, and Z. Zhang, "Delay-dependent robust stability and stabilization for uncertain discrete singular systems with time-varying delays," Journal of Comput. & Applied Math., vol. 217, no. 1, pp. 194-211, 2008. https://doi.org/10.1016/j.cam.2007.01.044
  11. Z. Wu, H. Su, and J. Chu, "Robust stabilization for uncertain discrete singular systems with state delay," International Journal of Robust & Nonlinear Control, vol. 18, pp. 1532-1550, 2008. https://doi.org/10.1002/rnc.1302
  12. W. Li, E. Todorov, and R. E. Skelton, "Estimation and control of systems with multiplicative noise via linear matrix inequalities," American Control Conference, Portland, OR, USA, pp. 1811-1816, 2005.
  13. X. M. Zhang and Q. L. Han, "Robust $H{\infty}$ filtering for uncertain discrete-time systems with timevarying delay based on a finite sum inequality," IEEE Trans. on Circuits and Systems II: Express Briefs, vol. 53, no. 12, pp. 1466-1470, 2006. https://doi.org/10.1109/TCSII.2006.884116