Limit Behavior of Reachable Sets of Linear Time-Invariant Systems with Integral Bounds on Control



In this paper, a linear dynamic system is considered under L p -constraint on control. We establish the existence of the limit shape of reachable sets as time goes to infinity. Asymptotic formulas are obtained for reachable sets and their shapes. The results throw a bridge between the cases of geometric bounds on control and constraints on the total impulse of control, and create a unified picture of the structure of the limit shapes of reachable sets.


Linear control systems Reachable sets Shapes of convex bodies 


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© Springer Science+Business Media New York 2012

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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