Linear Discrete-Time Systems - \(H_\infty \) Dynamic Output-Feedback Control with Preview

  • Eli GershonEmail author
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 613)


The theory of preview tracking control is applied for the solution of the dynamic output-feedback control problem of linear discrete-time systems for both: finite-horizon and stationary cases. Based of the solution of the state-feedback control problem and a specially devised version of the bounded real lemma for systems with tracking signals, three preview patterns are explored. The latter include the simplest case where the tracking signal is measured on line and two additional cases where the tracking signal is either previewed in a fixed interval ahead or it is perfectly known in advance along the finite horizon interval given in the system. The principle method of solution for all the latter three preview patterns is that the controller plays against nature which chooses the initial condition and the energy-bounded disturbances.


\(H_\infty \) control Discrete-time systems Tracking preview 


  1. 1.
    Gershon E (2018) \(H_\infty \) measurement-feedback tracking with preview. ICINCO, Porto, PortugalGoogle Scholar
  2. 2.
    Yang GH, Zhang XN (2008) Reliable \(H_{\infty }\) flight tracking control via state feedback. In: American control conference westin seattle hotel, pp 1800–1805Google Scholar
  3. 3.
    Luo W, Chu YC, Ling KV (2005) \(H_{\infty }\) inverse optimal attitude-tracking control of rigid spacecraft. J Guidance Control Dyn 28(3):481–494CrossRefGoogle Scholar
  4. 4.
    Kim BS, Tao TC (2002) An integrated feedforward robust repetitive control design for tracking near periodic time varying signals. Japan-USA on Flexible Automation, JapanGoogle Scholar
  5. 5.
    You WQ, Chen HH, He XD (2010) Tracking control research of high-order flexible structures on the H-infinity control method. In: 2nd international conference on advanced computer control (ICACC)Google Scholar
  6. 6.
    Wen G, Ugrinovskii V (2013) Distributed H-infinity tracking control for discrete-time multi-agent systems with a high-dimensional leader. In: Proceedings of the 52nd IEEE conference on decision and control, Florence, ItalyGoogle Scholar
  7. 7.
    Wu J, Nguang SK, Shen J, Liu G, Li YG (2010) Robust \(H_{\infty }\) tracking control of boiler-turbine systems. ISA Trans 49(3):369–375CrossRefGoogle Scholar
  8. 8.
    Gao H, Chen T (2008) Network-based \(H_{\infty }\) output tracking control. IEEE Trans Autom Control 53(3):655–667MathSciNetCrossRefGoogle Scholar
  9. 9.
    Shaked U, deSouza CE (1995) Continuous-time tracking problems in an \(H_{\infty }\) setting: a game theory approach. IEEE Trans Autom Control 40(5):841–852MathSciNetCrossRefGoogle Scholar
  10. 10.
    Gershon E, Shaked U, Yaesh I (2005) \(H_\infty \) control and estimation of state-multiplicative linear systems, vol 318. Lecture notes in control and information sciences, LNCIS. Springer, HeidelbergzbMATHGoogle Scholar
  11. 11.
    Gershon E, Shaked U (2013) Advanced topics in control and estimation of state-multiplicative noisy systems, vol 439. Lecture notes in control and information sciences, LNCIS. Springer, HeidelbergCrossRefGoogle Scholar
  12. 12.
    Gershon E, Shaked U, Berman N (2010) \(H_\infty \) preview tracking control for retarded stochastic systems. In: Conference on control and fault tollerant systems (SysTol10), Nice, FranceGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Holon Institute of Technology (HIT)HolonIsrael
  2. 2.Tel Aviv UniversityTel AvivIsrael

Personalised recommendations