Journal of Optimization Theory and Applications

, Volume 168, Issue 2, pp 615–624 | Cite as

Small-Time Reachable Sets of Linear Systems with Integral Control Constraints: Birth of the Shape of a Reachable Set

  • Elena Goncharova
  • Alexander Ovseevich


The paper is concerned with small-time reachable sets of a linear dynamical system under integral constraints on control. The main result is the existence of a limit shape of the reachable sets as time tends to zero. A precise estimate for the rate of convergence is given.


Linear control systems Reachable sets Shapes of convex bodies 

Mathematics Subject Classification

93B03 93B05 52A23 



This work was partially supported by the Russian Foundation for Basic Research, Grants 14-08-00606, 14-01-00476, 13-08-00441. We are grateful to anonymous referees for providing insightful comments and suggesting additional bibliography.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute for System Dynamics and Control TheorySiberian Branch of the Russian Academy of SciencesIrkutskRussia
  2. 2.Institute for Problems in Mechanics of the Russian Academy of SciencesMoscowRussia

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