Recovering nominal tracking performance in an asymptotic sense for uncertain linear systems

Gyunghoon Park, Hyungbo Shim, Youngjun Joo

Research output: Contribution to journalArticlepeer-review


In this paper, we consider the problem of recovering a (predefined) nominal output trajectory in the presence of model uncertainty and external disturbance. In particular, whereas the nominal performance recovery (NPR) has been studied in an approximate fashion in the literature, we extend the notion of the NPR in an asymptotic sense from the perspective of the internal model principle: that is, as long as the disturbance and reference signals are generated by an exogenous system, the actual output not only is kept close to the nominal trajectory as much as desired but also asymptotically converges to the nominal one as time elapses. It is shown via the singular perturbation theory that the asymptotic NPR can be achieved for uncertain minimum-phase systems under arbitrarily large (but bounded) model uncertainty. A disturbance observer (DOB) approach is employed in the controller design, with the internal model embedded into the so-called Q-filter, which is a key component of the DOB. Simulation results for mechanical positioning systems illustrate that the asymptotic NPR can enhance robust performance of control systems.

Original languageEnglish
Pages (from-to)700-722
Number of pages23
JournalSIAM Journal on Control and Optimization
Issue number2
StatePublished - 2018


  • Disturbance observer
  • Internal model principle
  • Nominal performance recovery
  • Robust control


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