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Robust ESPR analysis and control for uncertain continuous-time descriptor systems

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Abstract

In this paper, a strict linear matrix inequality (strict LMI) condition for extended strictly positive real (ESPR) characterization of continuous-time descriptor systems with norm-bounded uncertainty is addressed. Based on it, necessary and sufficient condition for dynamic output feedback controller such that robustly stabilize the uncertain descriptor system and make the entire class of uncertain closed-loop transfer matrices achieve the ESPR property is also derived. Finally, a numerical example is illustrated the proposed results.

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References

  1. S. L. Campbell, “A general method for nonlinear descriptor systems: an example for robotic path control,” Proc. of 27th IEEE CDC, pp. 630–631, 1988.

  2. A. Kumar and P. Daoutids, “Feedback control of nonlinear differential-algebraic equation systems,” AIChE Journal, vol. 41, no. 3, pp. 619–636, 1995.

    Article  Google Scholar 

  3. B. Benkatasubramanian, “On a singular transformation for analyzing the global dynamics of a class of singular DAE’s,” Proc. of SINS’92, pp. 364–371, 1992.

  4. L. Dai, Singular Control Systems-Lecture notes in Control and Information Sciences, Springer-Verlag, Berlin, 1989.

    Google Scholar 

  5. F. L. Lewis, “A tutorial on the geometric analysis of linear time-invariant implicit systems,” Automatica, vol. 28, no. 1, pp. 119–137, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. G. Wu and G. R. Duan, “Design of PD observer in descriptor linear systems,” Int. J. of Control, Automation, and Systems, vol. 5, no. 1, pp. 93–98, 2007.

    MathSciNet  Google Scholar 

  7. M. H. Moghaddam and H. Khaloozadeh, “Revision on the frequency domain conditions for strict positive realness,” Int. J. of Control, Automation, and Systems, vol. 5, no. 1, pp. 1–7, 2007.

    Google Scholar 

  8. W. M. Haddad and D. S. Bernstein, “Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. Part I: Continuous-time theory,” Int. J. Robust and Nonlinear Control, vol. 3, no. 4, pp. 313–339, 1993.

    Article  MATH  Google Scholar 

  9. H. S. Wang and F. R. Chang, “The generalized state-space description of positive realness and bounded realness,” Proc. IEEE 39th Midwest Symposium on Circuits and System, pp. 893–896, 1997.

  10. H. S. Wang, C. F. Yung, and F. R. Chang, “The positive real control problem and the generalized algebraic Riccati equation for descriptor systems,” Journal of the Chinese Institute of Engineerings, vol. 24, no. 2, pp. 203–220, 2001.

    Google Scholar 

  11. L. Zhang, J. Lam, and S. Xu, “On positive realness of descriptor systems,” IEEE Trans. Circuits Syst. I, vol. 49, no. 3, pp. 401–407, 2002.

    Article  MathSciNet  Google Scholar 

  12. A. Rehm and F. Allgöwer, “General quadratic performance analysis and synthesis of differential algebraic equation (DAE) systems,” Journal of Process Control, vol. 12, no. 4, pp. 467–474, 2002.

    Article  Google Scholar 

  13. L. Xie, “Output feedback H control of system with parameter uncertainty,” Int. J. Contr., vol. 63, no. 4, pp. 741–750, 1996.

    Article  MATH  Google Scholar 

  14. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, PA, 1994.

    MATH  Google Scholar 

  15. D. J. Bender and A. J. Laub, “The linear-quadratic optimal regulator for descriptor systems,” IEEE Trans. Automat. Contr., vol. 32, no. 8, pp. 672–688, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  16. P. Gahinet, A. Nemirovsky, A. J. Laub, and M. Chilali, LMI Control Toolbox User’s Guide, The MathWorks Inc., Mass., 1995.

    Google Scholar 

  17. I. Masubuchi, “Dissipativity inequalities for continuous-time descriptor systems with applications to synthesis of control gains,” Systems & Control Letters, vol. 55, no. 2, pp. 158–164, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  18. I. Masubuchi, “Output feedback controller synthesis for descriptor systems satisfying closed-loop dissipativity,” Automatica, vol. 43, no. 2, pp. 339–345, 2007.

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Jian Liung Chen.

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Recommended by Editorial Board member Duk-Sun Shim under the direction of Editor Jae Weon Choi.

Jian Liung Chen received the Ph.D. degree in Electrical Engineering from National Sun Yat-Sen University, Taiwan in 2003. Currently, he is an assistant professor of Department of Electrical Engineering, Kao-Yuan University, Lu-Chu Hsiang, Kaohsiung, Taiwan, where has been since 2005. His research interests include LMI approach in control, robust control, and descriptor system theory.

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Chen, J.L. Robust ESPR analysis and control for uncertain continuous-time descriptor systems. Int. J. Control Autom. Syst. 8, 8–15 (2010). https://doi.org/10.1007/s12555-010-0102-2

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  • DOI: https://doi.org/10.1007/s12555-010-0102-2

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