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P. 10
Simulation bandwidth control
Problem statement
Given 𝑥̇ = 𝐹 𝑥 , limit the bandwidth of the simulation to ωcut-off Solution
Linear approximation Eigenvalueplacement Practical realization
Eigenvalue placement
𝑥̇ = 𝐹 𝑥 → 𝑥̇ = 𝐽𝑥 + 𝑅(𝑥)
𝑥̇=𝐽𝑥+𝑅(𝑥)→ 𝑥̇=𝐽𝑥+𝑅(𝑥)
Solve
𝐽 𝑢 = 𝐹 𝑥 → Integrate 𝑥̇ = 𝐽 𝑢
Find eigenvalues and eigenvectors
Build by removing the imaginary parts of Build from
Presenter: Sergei Galkin
C O N F I D E N T I A L 10
of
that exceed ωcut-off
P R I V I L E G E D
A N D
