Quiet Standing of Time-Delay Stability with Derivative Feedback Control

  • Fitri Yakub
  • Ahmad Zahran Md. Khudzari
  • Yasuchika Mori
Conference paper


The published literature for stability analysis of linear time-delay systems has attracted much interest among the researchers over the last five decades. In general, the stability for linear time-delay systems can be checked exactly only by eigenvalue considerations. Two types of stability conditions are delay-independent type, mainly used for arbitrarily large delays, and delay-dependent type, which is mostly useful in applications that consider maximum delay. In this paper, we consider a linear time-invariant system with delay differential equation form for quiet-standing case study as a derivative feedback control. When it is reasonably chosen with intentional delays, the effects of time delay for ankle torque can be used to improve and stabilize the response of the close-loop systems.


Delay Differential Equation Inverted Pendulum Limit Cycle Oscillation Feedback Time Delay Quiet Stance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Sontag ED (2004) Some new directions in control theory inspired by systems biology. Syst Biol 1:9–18CrossRefGoogle Scholar
  2. 2.
    Bose A, Ioannou PA (2003) “Analysis of traffic flow with mixed manual and semi-automated vehicles”, IEEE Trans. Intell Transport Syst 4(4):173–188CrossRefGoogle Scholar
  3. 3.
    Treiber M, Kesting A, Helbing D (2006) Delays, inaccuracies and anticipation in microscopic traffic models. Phys A 360(1):71–88CrossRefGoogle Scholar
  4. 4.
    Baker CTH, Bocharov GA, Rihan FA (1999) A report on the use of delay differential equations in numerical modelling in the biosciences. Numerical analysis report, No. 343, Manchester, UK.
  5. 5.
    Logemann H, Townley S (1996) The effect of small delays in the feedback loop on the stability of neutral systems. Syst Contr Lett 27:267–274CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Frank TD, Friedrich R, Beek PJ (2005) Identifying and comparing states of time-delayed systems: phase diagrams and applications to human motor control systems. Phys Lett A 338:74–80CrossRefMATHGoogle Scholar
  7. 7.
    Niculescu S-I, Michiels W (2004) Stabilizing a chain of integrators using multiple delays. IEEE Trans Automat Contr 49:802–807CrossRefMathSciNetGoogle Scholar
  8. 8.
    Riddalls CE, Bennett S (2002) The stability of supply chains. Int J Prod Res 40:459–475CrossRefMATHGoogle Scholar
  9. 9.
    Sipahi F et al (2011) Stability and stabilization of systems with time delay. IEEE Contr Syst Mag 2011:38–49Google Scholar
  10. 10.
    Linh V, Morgansen KA (2010) Stability of time-delay feedback switched linear systems. IEEE Trans Automat Contr 55(10):2385–2390Google Scholar
  11. 11.
    Morasso PG, Schieppati M (1999) Can muscle stiffness alone stabilize upright standing? J Neurophysiol 83:1622–1626Google Scholar
  12. 12.
    Winter DA, Patla AE, Rietdyk S, Ishac MG (2001) Ankle muscle stiffness in the control of balance during quiet standing. J Neurophysiol 85:2630–2633Google Scholar
  13. 13.
    Schieppati M, Nardone EA (1997) Medium-latency stretch reflexes of foot and leg muscles analyzed by cooling the lower limb in standing humans. J Physiol 503:691–698CrossRefGoogle Scholar
  14. 14.
    Loram ID, Maganaris CN, Lakie M (2005) Active, non-spring-like muscle movements in human postural sway: how might paradoxical changes in muscle length be produced? J Physiol 564:281–293CrossRefGoogle Scholar
  15. 15.
    Fuglevand AJ, Winter DA, Patla AE (1993) Models of recruitment and rate coding organization in motor-unit pools. J Neurophysiol 70:2470–2488Google Scholar
  16. 16.
    Loram I, Lakie M (2002) Direct measurement of human ankle stiffness during quiet standing: the intrinsic mechanical stiffness is insufficient for stability. J Physiol 545:1041–1053CrossRefGoogle Scholar
  17. 17.
    Bottaro A et al (2008) Bounded stability of the quiet standing posture: an intermittent control model. Hum Mov Sci 27:473–495CrossRefGoogle Scholar

Copyright information

© Springer Japan 2015

Authors and Affiliations

  • Fitri Yakub
    • 1
    • 2
  • Ahmad Zahran Md. Khudzari
    • 3
  • Yasuchika Mori
    • 1
  1. 1.Graduate School of System DesignTokyo Metropolitan UniversityTokyoJapan
  2. 2.Malaysia-Japan International Institute of TechnologyUniversiti Teknologi MalaysiaKuala LumpurMalaysia
  3. 3.IJN-UTM Cardiovascular Engineering Centre, Faculty of Biosciences and Medical Engineering UTMJohor BahruMalaysia

Personalised recommendations