Skip to main content
SpringerLink
Log in

Input-to-state stability for a class of discrete-time nonlinear input-saturated switched descriptor systems with unstable subsystems

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This paper concerns the input-to-state stability (ISS) problems for a class of discrete-time nonlinear input-saturated switched descriptor systems (SDSs). An ISS criterion that only partial subsystems are exponentially stable is provided based on average dwell time method and discrete-time iterative algorithm. The proof difficulty is greatly decreased, and the switching controllers for the subsystems of the closed-loop SDSs are much simple and viable. Furthermore, the cost of the controllers is also greatly reduced. Finally, extensive simulation results are presented to illustrate the effectiveness of the developed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

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

Similar content being viewed by others

References

  1. Sun Z, Ge SS (2011) Stability theory of switched dynamical systems. Spring, London

    Book  MATH  Google Scholar 

  2. Boukas EK (2005) Stochastic switching systems: analysis and design. Birkhäuser, Boston

    Google Scholar 

  3. Restrepo C, Calvente J, Romero A, Vidal Idiarte E, Giral R (2012) Current-mode control of a coupled-inductor buck-boost DC-DC switching converter. IEEE Trans Power Electron 27(5):2536–2549

    Article  Google Scholar 

  4. Wu L, Shi P, Su X (2014) Sliding mode control of uncertain parameter-switching hybrid systems. Wiley, London

    Book  Google Scholar 

  5. Chattrejee D, Liberzon D (2007) On stability of randomly switched nonlinear systems. IEEE Trans Autom Control 52(12):2390–2394

    Article  MathSciNet  MATH  Google Scholar 

  6. Sen MD, Ibeas A (2008) Stability results for switched linear systems with constant discrete delays. Math Probl Eng 2008:1–28

    MathSciNet  MATH  Google Scholar 

  7. Sen MD, Ibeas A (2008) On the global asymptotic stability of switched linear time-varying with constant point delays. Discrete Dyn Nat Soc 2008:1–31

    MathSciNet  MATH  Google Scholar 

  8. Liu Y, Niu Y, Zou Y, Karimi HR (2015) Adaptive sliding mode reliable control for switched systems with actuator degradation. IET Control Theory Appl 9(8):1197–1204

    Article  MathSciNet  Google Scholar 

  9. Zhao X, Zhang L, Shi P (2013) Stability of a class of switched positive linear time-delay systems. Int J Robust Nonlinear Control 23(5):578–589

    Article  MathSciNet  MATH  Google Scholar 

  10. Niu B, Zhao J (2013) Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems. Syst Control Lett 62(10):963–971

    Article  MathSciNet  MATH  Google Scholar 

  11. Niu B, Zhao X, Yang X, Fan X (2015) Tracking and H ∞ control of constrained nonlinear switched systems in strict feedback form. Nonlinear Dyn 80(1):87–100

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhang L, Shi P (2009) Stability, l 2-gain and asynchronous H ∞ control of discrete-time switched systems with average dwell time. IEEE Trans Autom Control 54(9):2193–2200

    MathSciNet  Google Scholar 

  13. Ding D, Yang G (2010) H ∞ static output feedback control for discrete-time switched linear systems with average dwell time. IET Control Theory Appl 4(3):381–390

    Article  MathSciNet  Google Scholar 

  14. Zhao XD, Zhang LX, Shi P, Liu M (2012) Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Trans Autom Control 57(7):1809–1815

    Article  MathSciNet  MATH  Google Scholar 

  15. Niu B, Zhao J (2013) Robust H ∞ control for a class of uncertain nonlinear switched systems with average dwell time. Int J Control 86(6):1107–1117

    Article  MathSciNet  MATH  Google Scholar 

  16. Chen Y, Fei S, Zhang K (2012) Stabilization of impulsive switched linear systems with saturated control input. Nonlinear Dyn 69(3):793–804

    Article  MathSciNet  MATH  Google Scholar 

  17. Chen Y, Fei S, Zhang K (2014) Stabilisation for switched linear systems with time-varying delay and input saturation. Int J Syst Sci 45(3):532–546

    Article  MathSciNet  MATH  Google Scholar 

  18. Chen Y, Fei S, Li Y (2015) Stabilization of neutral time-delay systems with actuator saturation via auxiliary time-delay feedback. Automatica 52:242–247

    Article  MathSciNet  MATH  Google Scholar 

  19. Xu S, Lam J (2006) Robust control and filtering of singular systems. Springer, Berlin

    MATH  Google Scholar 

  20. Wang G, Zhang Q (2012) Robust control of uncertain singular stochastic systems with markovian switching via proportional-derivative state feedback. IET Control Theory Appl 6(8):1089–1096

    Article  MathSciNet  Google Scholar 

  21. Liu Y, Zhang C, Gao C (2012) Dynamic soft variable structure control of singular systems. Commun Nonlinear Sci Numer Simul 17(8):3345–3352

    Article  MathSciNet  MATH  Google Scholar 

  22. Liao F, Tomizuka M, Cao M, Wang D (2013) Optimal preview control for discrete-time descriptor causal systems in a multirate setting. Int J Control 86(5):844–854

    Article  MathSciNet  MATH  Google Scholar 

  23. Kao Y, Xie J, Wang C (2014) Stabilization of singular Markovian jump systems with generally uncertain transition rates. IEEE Trans Autom Control 59(9):2604–2610

    Article  MathSciNet  MATH  Google Scholar 

  24. Liu Y, Kao Y, Gu S, Karimi HR (2015) Soft variable structure controller design for singular systems. J Franklin Inst 352(4):1613–1626

    Article  MathSciNet  Google Scholar 

  25. Gao Z, Yang K, Shen Y, Ji Z (2015) Input-to-state stability analysis for a class of nonlinear switched descriptor systems. Int J Syst Sci 46(16):2973–2981

    Article  MathSciNet  MATH  Google Scholar 

  26. Xiong WJ, Ho DWC, Cao JD (2008) Synchronization analysis of singular hybrid coupled networks. Phys Lett A 372(44):6633–6637

    Article  MATH  Google Scholar 

  27. Liberzon D, Trenn S (2012) Switched nonlinear differential algebraic equations: solution theory, Lyapunov functions, and stability. Automatica 48(5):954–963

    Article  MathSciNet  MATH  Google Scholar 

  28. Koenig D, Marx B, Jacquet D (2008) Unknown input observers for switched nonlinear discrete time descriptor systems. IEEE Trans Autom Control 53(1):373–379

    Article  MathSciNet  MATH  Google Scholar 

  29. Long F, Xiao Y, Chen X, Zhang Z (2013) Disturbance attenuation for nonlinear switched descriptor systems based on neural network. Neural Comput Appl 23(7–8):2211–2219

    Article  Google Scholar 

  30. Zhao Y, Yang J, Wen G (2013) H ∞ control for uncertain switched nonlinear singular systems with time delay. Nonlinear Dyn 74(3):649–665

    Article  MathSciNet  MATH  Google Scholar 

  31. Xia Y, Boukas EK, Shi P, Zhang J (2009) Stability and stabilization of continuous-time singular hybrid systems. Automatica 45(6):1504–1509

    Article  MathSciNet  MATH  Google Scholar 

  32. Zamani I, Shafiee M, Ibeas A (2013) Stability analysis of hybrid switched nonlinear singular time-delay systems with stable and unstable subsystems. Int J Syst Sci 45(5):1128–1144

    Article  MathSciNet  MATH  Google Scholar 

  33. Zamani I, Shafiee M, Ibeas A (2013) Exponential stability of hybrid switched nonlinear singular systems with time-varying delay. J Franklin Inst 350(1):171–193

    Article  MathSciNet  MATH  Google Scholar 

  34. Lin JX, Fei SM, Gao ZF (2012) Stabilization of discrete-time switched singular time-delay systems under asynchronous switching. J Franklin Inst 349(5):1808–1827

    Article  MathSciNet  MATH  Google Scholar 

  35. Chen Y, Fei S, Zhang K (2013) Stability analysis for discrete-time switched linear singular systems: average dwell time approach. IMA J Math Control Inf 30(2):239–249

    Article  MathSciNet  MATH  Google Scholar 

  36. Liu Y, Kao Y, Karimi HR, Gao Z (2016) Input-to-state stability for discrete-time nonlinear switched singular systems. Inf Sci 358–359:18–28

    Article  Google Scholar 

  37. Zhu S, Shen Y (2013) Two algebraic criteria for input-to-state stability of recurrent neural networks with time-varying delays. Neural Comput Appl 22(6):1163–1169

    Article  Google Scholar 

  38. Xu Y, Luo W, Zhong K, Zhu S (2014) Mean square input-to-state stability of a general class of stochastic recurrent neural networks with Markovian switching. Neural Comput Appl 25(7):1657–1663

    Article  Google Scholar 

  39. Liu J, Liu X, Xie W (2012) Class-KL estimates and input-to-state stability analysis of impulsive switched systems. Syst Control Lett 61(6):738–746

    Article  MathSciNet  MATH  Google Scholar 

  40. Gao L, Wang D (2016) Input-to-state stability and integral input-to-state stability for impulsive switched systems with time-delay under asynchronous switching. Nonlinear Anal Hybrid Syst 20:55–71

    Article  MathSciNet  MATH  Google Scholar 

  41. Liu B, Hill DJ (2009) Input-to-state stability for discrete time-delay systems via the Razumikhin technique. Syst Control Lett 58(8):567–575

    Article  MathSciNet  MATH  Google Scholar 

  42. Kundu A, Chatterjee D, Liberzon D (2016) Generalized switching signals for input-to-state stability of switched systems. Automatica 64:270–277

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China under Grant 60974025, Shandong Province Natural Science Foundation under Grants ZR2015PE025 and ZR2012FL06, Shandong Province Higher Educational Science and Technology Program under Grants J16LB10 and J14LN52, and Weifang City Science and Technology Development Program under Grant 2014GX022.

Author information

Authors and Affiliations

  1. College of Information and Control Engineering, Weifang University, Weifang, 261061, People’s Republic of China

    Yunlong Liu, Juan Wang, Shuhong Tang & Zairui Gao

  2. Bureau of Economic Operation, Zoucheng Industrial Park Administration Commission, Jining, 273517, People’s Republic of China

    Juan Wang

  3. School of Mathematics Science, Ocean University of China, Qingdao, 266100, People’s Republic of China

    Cunchen Gao

Authors
  1. Yunlong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cunchen Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shuhong Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zairui Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yunlong Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Wang, J., Gao, C. et al. Input-to-state stability for a class of discrete-time nonlinear input-saturated switched descriptor systems with unstable subsystems. Neural Comput & Applic 29, 417–424 (2018). https://doi.org/10.1007/s00521-016-2519-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2519-x

Keywords

Search

Navigation