On the Equivalence of Extended and Oblique Projected Dynamics with Applications to Hybrid Integrator-Gain Systems

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The class of projected dynamical systems (PDS) provides a powerful framework for modeling dynamical systems of which the trajectories are constrained to a set by means of projection. This work is concerned with establishing equivalence results among two recent variations of PDS. These are (i) extended PDS (ePDS), which enable partial projection of dynamics, and (ii) oblique PDS, (oPDS) where projections can be done with respect to non-Euclidean norms. We present two sets of sufficient conditions for equivalence among these two system classes. These results enable the transfer of system theoretical properties and tools from one class to the other, which we illustrate in this paper. As an application, we study hybrid integrator-gain systems (HIGS), which are recently introduced hybrid control elements aiming at overcoming fundamental limitations of linear time-invariant control, and are formally described in the ePDS framework. We use our results to also describe these control elements as oPDS, thereby enabling the study of HIGS-controlled systems in this framework.

Original languageEnglish
Title of host publication2021 American Control Conference, ACC 2021
PublisherInstitute of Electrical and Electronics Engineers
Number of pages6
ISBN (Electronic)9781665441971
Publication statusPublished - 28 Jul 2021
Event2021 American Control Conference, ACC 2021 - Virtual, Virtual, New Orleans, United States
Duration: 25 May 202128 May 2021


Conference2021 American Control Conference, ACC 2021
Abbreviated titleACC 2021
Country/TerritoryUnited States
CityVirtual, New Orleans
Internet address

Bibliographical note

Funding Information:
Marcel Heertjes is also with ASML Mechatronic Systems Development, Veldhoven, the Netherlands. E-mail corresponding author: b.sharif@tue.nl This work is carried out as part of the project “From PID to complex order controller (CLOC)” and is supported by the Netherlands Organization for Scientific Research (NWO) Domain for Applied and Engineering Sciences (TTW).


  • Extended projected dynamical systems
  • hybrid integrator gain systems
  • oblique projected dynamical systems


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