slowfast

(Not recommended) Slow and fast modes decomposition

slowfast is not recommended. Use freqsep instead. (since R2023b) For more information on updating your code, see Version History.

Syntax

[G1,G2] = slowfast(G,ns)

Description

slowfast computes the slow and fast modes decompositions of a system G(s) such that

G(s) = [G₁(s)] + [G₂(s)]

G(s) contains the N slowest modes (modes with the smallest absolute value) of G.

$[G_{1} (s)] : = ({\hat{A}}_{11}, {\hat{B}}_{1}, {\hat{C}}_{1}, {\hat{D}}_{1})$ denotes the slow part of G(s). The slow poles have low frequency and magnitude values.

$[G_{2} (s)] : = ({\hat{A}}_{22}, {\hat{B}}_{2}, {\hat{C}}_{2}, {\hat{D}}_{2})$ denotes the fast part. The fast poles have high frequency and magnitude values.

The variable ns denotes the index where the modes will be split.

References

M.G. Safonov, E.A. Jonckheere, M. Verma and D.J.N. Limebeer, “Synthesis of Positive Real Multivariable Feedback Systems”, Int. J. Control, vol. 45, no. 3, pp. 817-842, 1987.

Version History

Introduced before R2006a

collapse all

R2023b: Not recommended

slowfast is not recommended. Use freqsep to separate slow and fast modes at a specified cutoff frequency instead of a specified number of modes.