Abstract and Applied Analysis

Reliable l2l and H Control for Nonlinear Singular Systems via Dynamic Output Feedback

Lin Li and Yuting Kang

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Abstract

The reliable l2l and H control for a class of Lipschitz nonlinear discrete-time singular systems with time delay is investigated via dynamic feedback control. The main goal of this paper is to design a generalized nonlinear controller such that, for possible actuator failures, the closed-loop system is regular, casual, and stable with a given l2l and H disturbance attenuation level being satisfied. Some sufficient conditions are obtained in terms of linear matrix inequalities (LMIs), and the controller design method is also proposed. Finally, a numerical example is included to illustrate the effectiveness of our proposed results.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 670543, 9 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412278132

Digital Object Identifier
doi:10.1155/2014/670543

Mathematical Reviews number (MathSciNet)
MR3193534

Citation

Li, Lin; Kang, Yuting. Reliable ${l}_{2}\text{–}{l}_{\mathrm{\infty }}$ and ${H}_{\mathrm{\infty }}$ Control for Nonlinear Singular Systems via Dynamic Output Feedback. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 670543, 9 pages. doi:10.1155/2014/670543. https://projecteuclid.org/euclid.aaa/1412278132


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References

  • H. H. Rosenbrock, “Structural properties of linear dynamical systems,” International Journal of Control, vol. 20, pp. 191–202, 1974.
  • S. H. Tan and J. Vandewalle, “Inversion of singular systems,” IEEE Transactions on Circuits and Systems, vol. 35, no. 5, pp. 583–587, 1988.
  • Q. L. Zhang, W. Q. Liu, and D. Hill, “A Lyapunov approach to analysis of discrete singular systems,” Systems & Control Letters, vol. 45, no. 3, pp. 237–247, 2002.
  • F. L. Lewis and D. W. Fountain, “Some singular systems applications in circuit theory,” IEEE Transactions on Circuits and Systems, vol. 2, pp. 1380–1384, 1990.
  • L. Li and L. Zhong, “Generalised nonlinear ${l}_{2}-{l}_{\infty }$ filtering of discrete-time markov jump descriptor systems,” International Journal of Control, vol. 87, no. 3, pp. 653–664, 2014.
  • L. Li, Z. Zhang, and J. Xu, “A generalized nonlinear ${H}_{\infty }$ filter design for discrete-time Lipschitz descriptor systems,” Nonlinear Analysis: Real World Applications, vol. 15, pp. 1–111, 2014.
  • J. Yao, Z. H. Guan, G. R. Chen, and D. W. C. Ho, “Stability, robust stabilization and ${H}_{\infty }$ control of singular-impulsive systems via switching control,” Systems & Control Letters, vol. 55, no. 11, pp. 879–886, 2006.
  • G. H. Yang and J. X. Dong, “Control synthesis of singularly perturbed fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 16, no. 3, pp. 615–629, 2008.
  • L. Li and Y. Jia, “Observer-based resilient ${L}_{2}-{L}_{\infty }$ control for singular time-delay systems,” IET Control Theory & Applications, vol. 3, no. 10, pp. 1351–1362, 2009.
  • Y. Zhou and J. Li, “Energy-to-peak filtering for singular systems: the discrete-time case,” IET Control Theory & Applications, vol. 2, no. 9, pp. 773–781, 2008.
  • L. Zhou, D. W. C. Ho, and G. Zhai, “Stability analysis of switched linear singular systems,” Automatica, vol. 49, no. 5, pp. 1481–1487, 2013.
  • J. Wang, H. Wang, A. Xue, and R. Lu, “Delay-dependent ${H}_{\infty }$ control for singular Markovian jump systems with time delay,” Nonlinear Analysis: Hybrid Systems, vol. 8, pp. 1–12, 2013.
  • Y. Feng and M. Yagoubi, “On state feedback ${H}_{\infty }$ control for discrete-time singular systems,” IEEE Transactions on Automatic Control, vol. 58, no. 10, pp. 2674–2679, 2013.
  • M. Chadli and M. Darouach, “Further enhancement on robust ${H}_{\infty }$ control design for discrete-time singular systems,” IEEE Transactions on Automatic Control, vol. 59, no. 2, pp. 494–499, 2012.
  • M. Abbaszadeh and H. J. Marquez, “A generalized framework for robust nonlinear ${H}_{\infty }$ filtering of Lipschitz descriptor systems with parametric and nonlinear uncertainties,” Automatica, vol. 48, no. 5, pp. 894–900, 2012.
  • X.-H. Chang and G.-H. Yang, “Non-fragile fuzzy ${H}_{\infty }$ filter design for nonlinear continuous-time systems with \emphD stability constraints,” Signal Processing, vol. 92, no. 2, pp. 575–586, 2012.
  • Z. Wang, G. Wei, and G. Feng, “Reliable ${H}_{\infty }$ control for discrete-time piecewise linear systems with infinite distributed delays,” Automatica, vol. 45, no. 12, pp. 2991–2994, 2009.
  • E. Tian, D. Yue, and C. Peng, “Reliable control for networked control systems with probabilistic actuator fault and random delays,” Journal of the Franklin Institute: Engineering and Applied Mathematics, vol. 347, no. 10, pp. 1907–1926, 2010.
  • H. Zhang, J. Wang, and Y. Shi, “Robust ${H}_{\infty }$ sliding-mode control for Markovian jump systems subject to intermittent observations and partially known transition probabilities,” Systems & Control Letters, vol. 62, no. 12, pp. 1114–1124, 2013.
  • H. Zhang, Y. Shi, and J. Wang, “On energy-to-peak filtering for nonuniformly sampled nonlinear systems: a markovian jump system approach,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 212–222, 2014.
  • H. Zhang, Y. Shi, A. S. Mehr, and H. Huang, “Robust FIR equalization for time-varying communication channels with intermittent observations via an LMI approach,” Signal Processing, vol. 91, no. 7, pp. 1651–1658, 2011.
  • H. Zhang, Y. Shi, and A. S. Mehr, “Robust ${H}_{\infty }$ PID control for multivariable networked control systems with disturbance/noise attenuation,” International Journal of Robust and Nonlinear Control, vol. 22, no. 2, pp. 183–204, 2012.
  • H. Zhang, Y. Shi, and A. S. Mehr, “On ${H}_{\infty }$ filtering for discrete-time Takagi-Sugeno fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 2, pp. 396–401, 2012.
  • L. Li, F. Li, Z. Zhang, and J. Xu, “On mode-dependent ${H}_{\infty }$ filtering for network-based discrete-time systems,” Signal Processing, vol. 93, no. 4, pp. 634–640, 2013.
  • H. Gao, J. Lam, L. Xie, and C. Wang, “New approach to mixed ${H}_{2}/{H}_{\infty }$ filtering for polytopic discrete-time systems,” IEEE Transactions on Signal Processing, vol. 53, no. 8, pp. 3183–3192, 2005.
  • J. Zhang, Y. Xia, and P. Shi, “Parameter-dependent robust ${H}_{\infty }$ filtering for uncertain discrete-time systems,” Automatica, vol. 45, no. 2, pp. 560–565, 2009. \endinput