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The delay-range-dependent robust stability analysis for 2-D state-delayed systems with uncertainty

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Abstract

This paper addresses the problems of delay-range-dependent stability and robust stability for uncertain two-dimensional (2-D) state-delayed systems in the Fornasini–Machesini second model, with the uncertainty assumed to be of norm bounded form. A generalized Lyapunov function candidate is introduced to prove the stability condition and some free-weighting matrices are used for less conservative conditions. The resulting stability and robust stability conditions in terms of linear matrix inequalities are delay-range-dependent. Some numerical examples are given to illustrate the method.

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References

  • Chen, S., & Fong, I. (2006). A delay-dependent approach to H ∞ filtering for 2-D state-delayed systems. In: Proceedings 45th IEEE conference on systems and control in aerospace and astronautics (pp. 540–544).

  • Chen S., Fong I. (2007) Delay-dependent robust H ∞ filtering for uncertain 2-D state-delayed systems. Signal Processing 87(11): 2659–2672

    Article  MATH  Google Scholar 

  • Feng Z., Xu L., Wu M., He Y. (2010) Delay-dependent robust stability and stabilisation of uncertain two-dimensional discrete systems with time-varying delays. IET Control Theory and Applications 10(4): 1959–1971

    Article  MathSciNet  Google Scholar 

  • He Y., Wang Q., Lin C., Wu M. (2007) Delay-range-dependent stability for systems with time-varying delay. Automatica 43(2): 371–376

    Article  MathSciNet  MATH  Google Scholar 

  • Hinamoto, T. (1989). The Fornasini–Marchesini model with no overflow oscillations and its application to 2-D digital filter design. In Proceedings IEEE international symposium on circuits and systems 1680–1683.

  • Mahmoud M. (2000) Robust control and filtering for time-delay systems. Control engineering series. Marcel Dekker, New York

    Google Scholar 

  • Paszke W., Lam J., Galkowski K., Xu S., Lin Z. (2004) Robust stability and stabilisation of 2D discrete state-delayed systems. Systems and Control Letters 51(3–4): 277–291

    Article  MathSciNet  MATH  Google Scholar 

  • Paszke, W., Lam, J., Galkowski, K., Xu, S., Rogers, E., & Kummert, A. (2006a). Delay-dependent stability of 2D state-delayed linear systems. In Proceedings IEEE international symposium on circuits and systems (pp. 2813–2816).

  • Paszke, W., Lam J., Galkowski, K., Xu, S., & Kummert, A. (2006b). Delay-dependent stability condition for uncertain linear 2-D state-delayed systems. In Proceedings 45th IEEE conference on decision and control (pp. 2783–2788).

  • Peng D., Guan X. (2009a) Output feedback H ∞ control for 2-D state-delayed systems. Circuits, Systems, and Signal Processing 28(1): 147–167

    Article  MathSciNet  MATH  Google Scholar 

  • Peng D., Guan X. (2009b) H ∞ filtering of 2-D discrete state-delayed systems. Multidimensional Systems and Signal Processing 20(3): 265–284

    Article  MathSciNet  MATH  Google Scholar 

  • Petersen I., Hollot C. (1986) A Riccati equation approach to the stabilization of uncertain linear systems. Automatica 22(4): 397–411

    Article  MathSciNet  MATH  Google Scholar 

  • Wu L., Wang Z., Gao H., Wang C. (2007) Filtering for uncertain 2-D discrete systems with state delays. Signal Processing 87(9): 2213–2230

    Article  MATH  Google Scholar 

  • Xie L., Lu L., Zhang D., Zhang H. (2004) Improved robust H 2 and H ∞ filtering for uncertain discrete-time systems. Automatica 40(5): 873–880

    Article  MathSciNet  MATH  Google Scholar 

  • Xu S., Lam J. (2005) Improved delay-dependent stability criteria for time-delay systems. IEEE Transactions on Automatic Control 50(3): 384–387

    Article  MathSciNet  Google Scholar 

  • Xu, H., Guo, L., Zou, Y., & Xu, S. (2007). Stability analysis for two-dimensional discrete delayed systems described by general models. In Proceedings IEEE international conference on control and automation (pp. 942–945).

  • Xu H., Xu S., Lam J. (2008) Positive real control for 2-D discrete delayed systems via output feedback controllers. Journal of Computational and Applied Mathematics 216(1): 87–97

    Article  MathSciNet  MATH  Google Scholar 

  • Xu J., Yu L. (2009a) Delay-dependent H ∞ control for 2-D discrete state delay systems in the second FM model. Multidimensional Systems and Signal Processing 20(4): 333–349

    Article  MathSciNet  Google Scholar 

  • Xu J., Yu L. (2009b) Delay-dependent guaranteed cost control for uncertain 2-D discrete systems with state delay in the FM second model. Journal of the Franklin Institute 346(2): 159–174

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang L., Wang C., Gao H. (2007) Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems. Journal of Systems Engineering and Electronics 18(2): 320–326

    Article  MATH  Google Scholar 

  • Zhu X., Yang G. (2008) Delay-dependent stability criteria for systems with differentiable time delays. Acta Automatica Sinica 34(7): 765–771

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China

    Juan Yao & Yun Zou

  2. Department of Mathematics, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China

    Weiqun Wang

Authors
  1. Juan Yao
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  2. Weiqun Wang
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  3. Yun Zou
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Correspondence to Juan Yao.

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Yao, J., Wang, W. & Zou, Y. The delay-range-dependent robust stability analysis for 2-D state-delayed systems with uncertainty. Multidim Syst Sign Process 24, 87–103 (2013). https://doi.org/10.1007/s11045-011-0156-1

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  • DOI: https://doi.org/10.1007/s11045-011-0156-1

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