Nonlinear Dynamics

, Volume 84, Issue 4, pp 2149–2160 | Cite as

Finite-time boundedness and dissipativity analysis of networked cascade control systems

  • K. Mathiyalagan
  • Ju H. Park
  • R. Sakthivel
Original Paper


In this paper, finite-time boundedness and dissipativity analysis for a class of networked cascade control systems (NCCSs) is investigated. The NCCS is defined with network-induced imperfections such as packet dropouts and time delays, and Bernoulli distributed white sequence is used to model a stochastic packet dropout case. Using the Lyapunov stability theory and linear matrix inequality (LMI) approach, we propose the sufficient conditions for finite-time boundedness and finite-time dissipativity of NCCS. Finally, the LMI-based conditions are applied on a practical power plant boiler–turbine system to show the effectiveness and applicability of the achieved results.


Cascade system Dissipativity Packet dropout Time delay Finite-time analysis 



The work of K. Mathiyalagan was supported by University Grants Commission (UGC), New Delhi, India, through Dr. D. S. Kothari Postdoctoral Fellowship under the Grant No. F.42/2006 (BSR)/MA/1415/0003, and the work of J. H. Park was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2013R1A1A2A 10005201).


  1. 1.
    Franks, R., Worley, C.: Quantitative analysis of cascade control. Ind. Eng. Chem. 48, 1074–1079 (1956)CrossRefGoogle Scholar
  2. 2.
    Du, Z., Yue, D., Hu, S.: H-infinity stabilization for singular networked cascade control systems with state delay and disturbance. IEEE Trans. Ind. Inf. 10, 1551–3203 (2014)Google Scholar
  3. 3.
    Huang, C., Bai, Y., Liu, X.: H-infinity state feedback control for a class of networked cascade control systems with uncertain delay. IEEE Trans. Ind. Inf. 6, 62–72 (2010)CrossRefGoogle Scholar
  4. 4.
    Wai, R., Kuo, M., Lee, J.: Design of cascade adaptive fuzzy sliding-mode control for nonlinear two-axis inverted-pendulum servomechanism. IEEE Trans. Fuzzy Syst. 16, 1232–1244 (2008)CrossRefGoogle Scholar
  5. 5.
    Guo, C., Song, Q., Cai, W.: A neural network assisted cascade control system for air handling unit. IEEE Trans. Ind. Electron. 54, 620–628 (2007)CrossRefGoogle Scholar
  6. 6.
    Demirel, B., Briat, C., Johansson, M.: Deterministic and stochastic approaches to supervisory control design for networked systems with time-varying communication delays. Nonlinear Anal. Hybrid Syst. 10, 94–110 (2013)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Mathiyalagan, K., Lee, T.H., Park, J.H., Sakthivel, R.: Robust passivity based resilient \({\cal {H}}_{\infty }\) control for networked control systems with random gain fluctuations. Int. J. Robust Nonlinear Control 26, 426–444 (2016)Google Scholar
  8. 8.
    Mathiyalagan, K., Park, J.H., Jung, H.Y., Sakthivel, R.: Non-fragile observer-based \({\cal {H}}_{\infty }\) control for discrete-time systems using passivity theory. Circuits Syst. Signal Proc. 34, 2499–2516 (2015)Google Scholar
  9. 9.
    Millan, P., Orihuela, L., Vivas, C., Rubio, F.R.: Distributed consensus-based estimation considering network induced delays and dropouts. Automatica 48, 2726–2729 (2012)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Zhang, W.A., Yu, L., Yin, S.: A switched system approach to \({\cal {H}}_{\infty }\) control of networked control systems with time-varying delays. J. Frankl. Inst. 348, 165–178 (2011)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Fadaei, A., Salahshoor, K.: Evaluation study of the transmission delay effects in a practical networked cascade control system. In: Proceedings of 16th Mediterranean Conference on Control and Automation Congress Centre, France, pp. 1598–1603 (2008)Google Scholar
  12. 12.
    Lee, T.H., Park, J.H., Lee, S.M., Kwon, O.M.: Robust sampled-data control with random missing data scenario. Int. J. Control 87, 1957–1969 (2014)Google Scholar
  13. 13.
    Zhang, W.A., Yu, L.: Modelling and control of networked control systems with both network-induced delay and packet-dropout. Automatica 44, 3206–3210 (2008)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Zhang, C., Feng, G., Qiu, J., Shen, Y.: Control synthesis for a class of linear network-based systems with communication constraints. IEEE Trans. Ind. Electron. 60, 3339–3348 (2013)Google Scholar
  15. 15.
    Yang, H., Knag, Y., Kuang, S.: Predictive compensation for networked cascade control systems with uncertainties. In: Proceedings of 31st Chinese Control Conference, Hefei, pp. 4256–4260 (2012)Google Scholar
  16. 16.
    Luo, W., Soares, C.G., Zou, Z.: Neural-network- and \({\cal {L}}_2\)-gain-based cascaded control of underwater robot thrust. IEEE J. Oceanic Eng. 39, 630–640 (2014)Google Scholar
  17. 17.
    Kottenstette, N., Hall III, J.F., Koutsoukos, X., Sztipanovits, J., Antsaklis, P.: Design of networked control systems using passivity. IEEE Trans. Control Syst. Technol. 21, 649–665 (2013)CrossRefGoogle Scholar
  18. 18.
    Willems, J.C.: Dissipative dynamical systems-part 1: general theory. Arch. Ration. Mech. Anal. 45, 321–351 (1972)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Willems, J.C.: Dissipative dynamical systems-part 2: linear systems with quadratic supply rates. Arch. Ration. Mech. Anal. 45, 352–393 (1972)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Hill, D.J., Moylan, P.J.: Stability of nonlinear dissipative systems. IEEE Trans. Autom. Control 21, 708–711 (1976)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Hill, D.J., Moylan, P.J.: Dissipative dynamical systems: basic input–output and state properties. J. Frankl. Inst. 309, 327–357 (1980)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Shen, H., Wu, Z.G., Park, J.H.: Finite-time energy-to-peak filtering for Markov jump repeated scalar non-linear systems with packet dropouts. IET Control Theory Appl. 8, 1617–1624 (2014)Google Scholar
  23. 23.
    Wang, S., Shi, T., Zhang, L., Jasra, A., Zeng, M.: Extended finite-time \({\cal {H}}_{\infty }\) control for uncertain switched linear neutral systems with time-varying delays. Neurocomputing 152, 377–387 (2015)Google Scholar
  24. 24.
    Yin, J., Khoo, S., Man, Z., Yu, X.: Finite-time stability and instability of stochastic nonlinear systems. Automatica 47, 2671–2677 (2011)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Zuo, Z., Li, H., Wang, Y.: New criterion for finite-time stability of linear discrete-time systems with time-varying delay. J. Frankl. Inst. 350, 2745–2756 (2013)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Liu, H., Zhao, X., Zhang, H.: New approaches to finite-time stability and stabilization for nonlinear system. Neurocomputing 138, 218–228 (2014)CrossRefGoogle Scholar
  27. 27.
    Du, H., Cheng, Y., He, Y., Jia, R.: Finite-time output feedback control for a class of second-order nonlinear systems with application to DC–DC buck converters. Nonlinear Dyn. 78, 2021–2030 (2014)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Wang, H., Han, Z., Xie, Q., Zhang, W.: Finite-time chaos control of unified chaotic systems with uncertain parameters. Nonlinear Dyn. 55, 323–328 (2009)MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Shen, H., Park, J.H., Wu, Z.G.: Finite-time reliable \(L_2\)-\(L_{\infty }/{\cal {H}}_{\infty }\) control for Takagi–Sugeno fuzzy systems with actuator faults. IET Control Theory Appl. 8, 688–696 (2014)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Zhang, Y., Shi, P., Nguang, S.K.: Observer-based finite-time \({\cal {H}}_{\infty }\) control for discrete singular stochastic systems. Appl. Math. Lett. 38, 115121 (2014)MathSciNetGoogle Scholar
  31. 31.
    Li, S., Tian, Y.P.: Finite-time stability of cascaded time-varying systems. Int. J. Control 80, 646–657 (2007)MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Huang, C., Bai, Y., Li, X.: Fundamental issues in networked cascade control systems. In: Proceedings of the IEEE International Conference on Automation and Logistics, Qingdao, pp. 314–3018 (2008)Google Scholar
  33. 33.
    Boyd, B., Ghoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of MathematicsBharathiyar UniversityCoimbatoreIndia
  2. 2.Department of Electrical EngineeringYeungnam UniversityKyongsanRepublic of Korea
  3. 3.Department of MathematicsSungkyunkwan UniversitySuwonRepublic of Korea

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