Skip to main content
Log in

Exponential H Output Tracking Control for Switched Neutral System with Time-Varying Delay and Nonlinear Perturbations

Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, the problem of exponential H output tracking control is addressed for a class of switched neutral system with time-varying delay and nonlinear perturbations. The considered system consists of different neutral and discrete delays. By resorting to the average dwell time approach, a new Lyapunov–Krasovskii functional is proposed to establish sufficient conditions for the exponential stability and H performance of switched neutral systems. Then, the problem of exponential H output tracking control is investigated, an explicit expression for the desired exponential tracking controller is also given. Finally, a numerical example is provided to demonstrate the potential effectiveness of the proposed method.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. L.I. Allerhand, U. Shaked, Robust stability and stabilization of linear switched systems with dwell time. IEEE Trans. Autom. Control 56(2), 381–386 (2011)

    Article  MathSciNet  Google Scholar 

  2. M.S. Branicky, Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control 43(4), 475–482 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. L. Crocco, Aspects of combustion stability in liquid propellant rocket motors, part I: fundamentals low frequency instability with monopropellants. J. Am. Rocket Soc. 21, 163–178 (1951)

    Google Scholar 

  4. D. Du, B. Jiang, P. Shi, S. Zhou, H filtering of discrete-time switched systems with state delays via switched Lyapunov function approach. IEEE Trans. Autom. Control 52(8), 1520–1525 (2007)

    Article  MathSciNet  Google Scholar 

  5. K.K. Fan, C.H. Lien, J.G. Hsieh, Asymptotic stability for a class of neutral systems with discrete and distributed time delays. J. Optim. Theory Appl. 114(3), 705–716 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. N.H. El Farral, P. Mhaskar, P.D. Christofides, Output feedback control of switched nonlinear systems using multiple Lyapunov functions. Syst. Control Lett. 54(1), 1163–1182 (2005)

    Article  Google Scholar 

  7. Y.A. Fiagbedzi, A.E. Pearson, A multistage reduction technique for feedback stabilizing distributed time-lag systems. Automatica 23(3), 311–326 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  8. Q.L. Han, On stability of linear neutral systems with mixed time delays: a discretized Lyapunov functional approach. Automatica 41(7), 1209–1218 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Q.L. Han, A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays. Automatica 40(10), 1791–1796 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Q.L. Han, Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica 41(12), 2171–2176 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. L. Hou, G. Zong, Y. Wu, Y. Cao, Exponential l 2l output tracking control for discrete-time switched system with time-varying delay. Int. J. Robust Nonlinear Control (2011). doi:10.1002/rnc.1743

    Google Scholar 

  12. C. Hua, X. Guan, P. Shi, Robust output feedback tracking control for time-delay nonlinear systems using neural network. IEEE Trans. Neural Netw. 17(2), 495–505 (2007)

    Article  Google Scholar 

  13. H.K. Khalil, Nonlinear Systems (Upper Saddle River, Prentice-Hall, 1996)

    Google Scholar 

  14. J. Lam, H. Gao, S. Xu, C. Wang, H and L 2/L model reduction for system input with sector nonlinearities. J. Optim. Theory Appl. 125(1), 137–155 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Q.K. Li, G.M. Dimirovski, J. Zhao, Robust tracking control for switched linear systems with time-varying delays, in Proceedings of the American Control Conference, Westin Seattle Hotel, Seattle, WA, USA (2008), pp. 1576–1581

    Google Scholar 

  16. Q.K. Li, G.M. Dimirovski, J. Zhao, Tracking control for switched time-varying delays systems with stabilizable and unstabilizable subsystems. Nonlinear Anal. Hybrid Syst. 3(2), 133–142 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Q.K. Li, J. Zhao, G.M. Dimirovski, Robust tracking control for switched linear systems with time-varying delays. IET Control Theory Appl. 2(6), 449–457 (2008)

    Article  MathSciNet  Google Scholar 

  18. Q.K. Li, J. Zhao, X.J. Liu, G.M. Dimirovski, Observer-based tracking control for switched linear systems with time-varying delay. Int. J. Robust Nonlinear Control 21(3), 309–327 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. D. Liberzon, Switching in Systems and Control (Birkhäuser, Basel, 2003)

    Book  MATH  Google Scholar 

  20. C.H. Lien, K.W. Yu, Non-fragile H control for uncertain neutral systems with time-varying delays via the LMI optimization approach. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 37(2), 493–499 (2007)

    Article  Google Scholar 

  21. C.H. Lien, K.W. Yu, J.G. Hsieh, Stability conditions for a class of neutral systems with multiple time delays. J. Math. Anal. Appl. 245(1), 20–27 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  22. Z.H. Qu, J. Dorsey, Robust tracking control of robots by a linear feedback law. IEEE Trans. Autom. Control 36(9), 1081–1084 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  23. J.P. Richard, Time-delay systems: an overview of some recent advances and open problems. Automatica 39(10), 1667–1694 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  24. X.M. Sun, J. Zhao, D.J. Hill, Stability and L 2-gain analysis for switched delay systems: a delay-dependent method. Automatica 42(5), 1769–1774 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  25. Z. Wang, W.C.H. Daniel, Filtering on nonlinear time-delay stochastic systems. Automatica 39(1), 101–109 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  26. S. Xu, T. Chen, Robust H control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers. Syst. Control Lett. 51(3–4), 171–183 (2004)

    Article  MATH  Google Scholar 

  27. L. Yu, S. Fei, X. Li, Robust adaptive neural tracking control for a class of switched affine nonlinear systems. Neurocomputing 73(10–12), 2274–2279 (2010)

    Article  Google Scholar 

  28. L. Yu, S. Fei, H. Zu, X. Li, Direct adaptive neural control with sliding mode method for a class of uncertain switched nonlinear systems. Int. J. Innov. Comput., Inf. Control 6(12), 5609–5618 (2010)

    Google Scholar 

  29. G.S. Zhai, B. Hu, K. Yasuda, A.N. Michel, Disturbance attenuation properties of time-controlled switched systems. J. Franklin Inst. 338(7), 765–779 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  30. L.X. Zhang, E.K. Boukas, P. Shi, Exponential H filtering for uncertain discrete-time switched linear systems with average dwell time: a μ-dependent approach. Int. J. Robust Nonlinear Control 18(11), 1188–1207 (2008)

    Article  MathSciNet  Google Scholar 

  31. X.M. Zhang, Q.L. Han, Stability analysis and H filtering for delay differential systems of neutral type. IET Control Theory Appl. 1(3), 749–755 (2007)

    Article  MathSciNet  Google Scholar 

  32. D. Zhang, L. Yu, H output tracking control for neural systems with time-varying delay and nonlinear perturbations. Commun. Nonlinear Sci. Numer. Simul. 15(11), 3284–3292 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  33. X.Q. Zhao, Y.Z. Liu, G.X. Zhong, M. Zhao, A less conservative result of H output tracking control for neutral systems with time-varying delay and nonlinear perturbations, in Proceedings of the Chinese Control and Decision Conference, Mianyang, 23–25 (2011), pp. 509–514

    Google Scholar 

  34. G.X. Zhong, Z.D. Xu, H.M. Wang, H output tracking control for neutral systems with time-varying delay and nonlinear perturbations: an LMI approach, in Proceedings of the Chinese Control and Decision Conference, Mianyang, 23–25 (2011), pp. 544–549

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No. 60974027 and NUST Research Funding (2011YBXM26).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhengrong Xiang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, S., Xiang, Z. Exponential H Output Tracking Control for Switched Neutral System with Time-Varying Delay and Nonlinear Perturbations. Circuits Syst Signal Process 32, 103–121 (2013). https://doi.org/10.1007/s00034-012-9450-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-012-9450-x

Keywords

Navigation