Asymptotic and probabilistic perturbation analysis of controllable subspaces

HIGHLIGHTS

• What: The authors are interested in the sensitivity to small parameter perturbations of the controllable subspaces of single-input time-invariant linear control systems, described by the state equation ẋ (t)=Ax (t) + Bu(t), where x ∈ Rn is the state vector, u ∈ R1 is the control vector and A ∈ Rn×n, B ∈ Rn×1. In Figure 3, the authors compare the asymptotic bound δU lin and the probabilistic estimate δU prob with the actual component-wise perturbations |δU | for normal distribution of perturbation entries and probabilities P re f=90%, 80% and 60%. Since the bounds . . .
  

   

  

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