# slowfast

Slow and fast modes decomposition

## 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.

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

$\left[{G}_{2}\left(s\right)\right]:=\left({\stackrel{^}{A}}_{22},{\stackrel{^}{B}}_{2},{\stackrel{^}{C}}_{2},{\stackrel{^}{D}}_{2}\right)$ 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.

Use freqsep to separate slow and fast modes at a specified cutoff frequency instead of a specified number of modes.

## 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