Controller design for nonlinear time delay distributed control systems subjected to input saturation nonlinearity and disturbances

  • Muntazir HussainEmail author
  • M. Siddique
  • M. Usman Hashmi
  • M. Taskeen Raza


This article proposes a state feedback controller synthesis for nonlinear time-delay distributed control systems subjected to input saturation nonlinearity and disturbances. Nonlinear time-delay distributed control system individual states are without time-delay and the states coming from other subsystems have the communication link time-delay. The coupling states time-delay is presumed to be time-varying within a predefined bound. First, we suggest global state feedback controller design and then, we extend the proposed global design technique to more general local state feedback controller scheme by using an auxiliary region of attraction. Linear matrix inequality (LMI)-based solution is anticipated to synthesis global and local state feedback controller by using global and local sector bounded condition, Lyapunov–Krasovskii function, and Lipschitz condition. Which guarantee global and local asymptotic stability of the complete closed-loop system and \( L_{2} \) gain reduction of the mapping from \( d_{p} (t) \) to \( z_{p} (t) \). Application results are presented to validate the benefits and effectiveness of the anticipated controller design schemes.


State feedback control Linear matrix inequalities (LMI) Lipschitz nonlinearity Nonlinear time-delay distributed control systems Sector bounded condition 


  1. 1.
    Tipsuwan Y, Chow MY (2003) Control methodologies in networked control systems. Control Eng Pract 11(10):1099–1111CrossRefGoogle Scholar
  2. 2.
    Branicky MS, Liberatore V, Phillips SM (2003) Networked control system co-simulation for co-design. IEEE Am Control Conf 4:3341–3346Google Scholar
  3. 3.
    D’Andrea R, Dullerud GE (2003) Distributed control design for spatially interconnected systems. IEEE Trans Autom Control 48(9):1478–1495MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Antsaklis P, Baillieul J (2007) Special issue on technology of networked control systems. Proc IEEE 95(1):5–8CrossRefGoogle Scholar
  5. 5.
    Song YQ (2009) Networked control systems: from independent designs of the network QoS and the control to the co-design. IFAC Proc Vol 42(3):155–162CrossRefGoogle Scholar
  6. 6.
    Nguyen XH, Juanole G (2012) Design of networked control systems (NCSs) on the basis of interplays between quality of control and quality of service. In: IEEE international symposium on industrial embedded systems (SIES), IEEE, pp 85–93Google Scholar
  7. 7.
    Donkers MCF, Heemels WPMH, Van de Wouw N, Hetel L (2011) Stability analysis of networked control systems using a switched linear systems approach. IEEE Trans Autom Control 56(9):2101–2115MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Liu K, Fridman E, Hetel L (2014) Networked control systems: a time-delay approach. In: IEEE european control conference (ECC), pp 1434–1439Google Scholar
  9. 9.
    Hussain M, Rehan M (2016) Nonlinear time-delay anti-windup compensator synthesis for nonlinear time-delay systems: a delay-range-dependent approach. Neurocomputing 186:54–65CrossRefGoogle Scholar
  10. 10.
    Yan H, Zhang H, Meng MQH (2010) Delay-range-dependent robust H∞ control for uncertain systems with interval time-varying delays. Neurocomputing 73(7):1235–1243CrossRefGoogle Scholar
  11. 11.
    He Y, Wang QG, Lin C, Wu M (2007) Delay-range-dependent stability for systems with time-varying delay. Automatica 43(2):371–376MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Li H, Shi Y (2013) Distributed model predictive control of constrained nonlinear systems with communication delays. Syst Control Lett 62(10):819–826MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Hussain M, us Saqib N, Rehan M (2016) Nonlinear dynamic regional anti-windup compensator (RAWC) schema for constrained nonlinear systems. In: IEEE international conference on emerging technologies (ICET), pp 1–6Google Scholar
  14. 14.
    Hussain M, Rehan M, Ahn CK, Tufail M (2018) Robust anti-windup for one-sided lipschitz systems subject to input saturation and applications. IEEE Trans Ind Electron. Google Scholar
  15. 15.
    Kapila V, Haddad WM (1998) Memoryless H controllers for discrete-time systems with time delay. Automatica 34(9):1141–1144CrossRefzbMATHGoogle Scholar
  16. 16.
    Kim JH, Park HB (1999) H state feedback control for generalized continuous/discrete time-delay system. Automatica 35(8):1443–1451MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Xu S, Lam J, Yang C (2001) H/sub/spl infin//and positive-real control for linear neutral delay systems. IEEE Trans Autom Control 46(8):1321–1326CrossRefzbMATHGoogle Scholar
  18. 18.
    Yu L, Chu J, Su H (1996) Robust memoryless H controller design for linear time-delay systems with norm-bounded time-varying uncertainty. Automatica 32(12):1759–1762MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    De Souza CE, Li X (1999) Delay-dependent robust H control of uncertain linear state-delayed systems. Automatica 35(7):1313–1321MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Fridman E, Shaked U (2002) A descriptor system approach to H/sub/spl infin//control of linear time-delay systems. IEEE Trans Autom Control 47(2):253–270CrossRefzbMATHGoogle Scholar
  21. 21.
    Fridman E, Shaked U (2002) An improved stabilization method for linear time-delay systems. IEEE Trans Autom Control 47(11):1931–1937MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Xu S, Lam J, Zou Y (2006) New results on delay-dependent robust H control for systems with time-varying delays. Automatica 42(2):343–348MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Zhang F (ed) (2006) The Schur complement and its applications, vol 4. Springer, BerlinGoogle Scholar
  24. 24.
    Li H, Shi Y (2014) Robust distributed model predictive control of constrained continuous-time nonlinear systems: a robustness constraint approach. IEEE Trans Autom Control 59(6):1673–1678CrossRefGoogle Scholar
  25. 25.
    Dunbar WB, Murray RM (2006) Distributed receding horizon control for multi-vehicle formation stabilization. Automatica 42(4):549–558MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Keviczky T, Borrelli F, Balas GJ (2006) Decentralized receding horizon control for large scale dynamically decoupled systems. Automatica 42(12):2105–2115MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Li H, Shi Y (2012) State-feedback H control for stochastic time-delay nonlinear systems with state and disturbance-dependent noise. Int J Control 85(10):1515–1531MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Yan H, Huang X, Wang M, Zhang H (2006) Delay-independent criteria for robust stability of uncertain networked control systems with multiple state time-delays. In: IEEE international conference on mechatronics and automation, pp 707–712Google Scholar
  29. 29.
    Yan H, Huang X, Wang M, Zhang H (2006) Delay-dependent robust stability of networked control systems with uncertainties and multiple time-varying delays. In: ieee international conference on mechatronics and automation, pp 373–378Google Scholar
  30. 30.
    Raghavan S, Hedrick JK (1994) Observer design for a class of nonlinear systems. Int J Control 59(2):515–528MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Rajamani R (1998) Observers for Lipschitz nonlinear systems. IEEE Trans Autom Control 43(3):397–401MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Torkamani S, Butcher EA (2013) Delay, state, and parameter estimation in chaotic and hyperchaotic delayed systems with uncertainty and time-varying delay. Int J Dyn Control 1(2):135–163CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Muntazir Hussain
    • 1
    Email author
  • M. Siddique
    • 2
  • M. Usman Hashmi
    • 1
  • M. Taskeen Raza
    • 3
  1. 1.Department of Electronic EngineeringIQRA UniversityIslamabadPakistan
  2. 2.Department of Electrical EngineeringNFC Institute of E&TMultanPakistan
  3. 3.Department of Electrical EngineeringLahore College for Women UniversityJhang PunjabPakistan

Personalised recommendations