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Estimates of the Minimal Eigenvalue of the Controllability Gramian for a System Containing a Small Parameter

  • Mikhail GusevEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11548)

Abstract

We consider a linear time-invariant control system with right-hand side depending on a small parameter. Assuming that the system is controllable, we study the asymptotics of the minimal eigenvalue of a system’s controllability Gramian and provide some bounds for the eigenvalue. These estimates are applied to the study of convexity properties of reachable sets for nonlinear control systems with integral constraints on control variables.

Keywords

Control system Controllability Gramian Small parameter Reachable set Integral constraints 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.N.N. Krasovskii Institute of Mathematics and MechanicsEkaterinburgRussia
  2. 2.Ural Federal UniversityEkaterinburgRussia

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