Disturbance attenuation in LTI plants with finite horizon: Optimality of nonlinear controllers

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It is an established fact that search for an optimum in the problem of disturbance attenuation in linear time-invariant (LTI) plants can be restricted to linear designs when the sole criterion is the minimization of the H-norm of an appropriate input-output operator. What is not known, however, is whether there exist also optimal nonlinear controllers which would lead to uniformly better performance (than linear controllers) in a neighborhood of the worst-case disturbance. It is shown in this paper that for the finite-horizon version, and with the disturbance energy fixed, there do exist optimal (minimax) controllers outside the linear class, which can oout-perform the best linear controller locally. It is also argued that a differential (dynamic) games set-up provides a natural framework for the time-domain derivation of optimal (minimax) controllers for tracking, model matching and disturbance rejection problems, in both finite and infinite horizons.

Original languageEnglish (US)
Pages (from-to)183-191
Number of pages9
JournalSystems and Control Letters
Issue number3
StatePublished - Sep 1989


  • H-optimal control
  • differential games
  • disturbance attenuation
  • minimax control
  • nonlinear controller
  • robust control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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