Hybrid dynamical systems with controlled discrete transitions

Joseph Bentsman, Boris M. Miller, Evgeny Ya Rubinovich, Kai Zheng

Research output: Contribution to journalArticlepeer-review


This invited survey focuses on a new class of systems-hybrid dynamical systems with controlled discrete transitions. A type of system behavior referred to as the controlled infinitesimal dynamics is shown to arise in systems with widely divergent dynamic structures and application domains. This type of behavior is demonstrated to give rise to a new dynamic mode in hybrid system evolution-a controlled discrete transition. Conceptual and analytical frameworks for modeling of and controller synthesis for such transitions are detailed for two systems classes: one requiring bumpless switching among controllers with different properties, and the other-exhibiting single controlled impacts and controlled impact sequences under collision with constraints. The machinery developed for the latter systems is also shown to be capable of analysing the behavior of difficult to model systems characterized by accumulation points, or Zeno-type behavior, and unique system motion extensions beyond them in the form of sliding modes along the constraint boundary. The examples considered demonstrate that dynamical systems with controlled discrete transitions constitute a general class of hybrid systems.

Original languageEnglish (US)
Pages (from-to)466-481
Number of pages16
JournalNonlinear Analysis: Hybrid Systems
Issue number4
StatePublished - Dec 2007


  • Accumulation points
  • Controlled discrete transitions
  • Controlled infinitesimal dynamics
  • Controller switching
  • Differential equations with a measure
  • Multi-impacts
  • Phase constraints

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Analysis
  • Computer Science Applications


Dive into the research topics of 'Hybrid dynamical systems with controlled discrete transitions'. Together they form a unique fingerprint.

Cite this