Achieving nonvanishing stability regions with high-gain cheap control using H techniques: The second-order case

G. J. Toussaint, T. Başar

Research output: Contribution to journalArticlepeer-review


This paper demonstrates how to use an asymptotically H-optimal controller to stabilize a second-order system subject to unknown disturbances such that the stability region does not vanish as the feedback gains increase. The high-gain feedback arises when one attempts to achieve the lowest achievable limit of the disturbance attenuation under the H design. This type of gain increase can cause the stability region to vanish if the disturbance contains nonlinear terms. The analysis using Lyapunov techniques derives a sufficient condition on the design parameters to prevent the stability region from vanishing. In addition to describing exact solutions for six different cases, the paper provides simulations to illustrate the results.

Original languageEnglish (US)
Pages (from-to)79-89
Number of pages11
JournalSystems and Control Letters
Issue number2
StatePublished - Oct 5 2001


  • Asymptotic stability regions for nonlinear systems
  • H control
  • Lyapunov methods

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science(all)
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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