tfm2ss (Robust Control Toolbox)

Convert a transfer function matrix (MIMO) into state-space form.

[a,b,c,d] = tfm2ss(num,den,r,c) 
[ss] = tfm2ss(tf,r,c)

Description
Tfm2ss converts a transfer function matrix G(s) of dimension r by c into the block-controller form [1], where

and d(s) is the least common multiple of the denominators of the entries of G(s)

and the entry in the ith row, jth column of the numerator matrix

The input variables num and den are of the following forms

where

A dual realization lock-observer form can simply be obtained by applying tfm2ss to GT(s), then taking the transpose of the resulting state-space system.

Note that the resulting system has n by c states and is not necessarily minimal. Model reduction routines such as minreal, schmr, ohklmr, or bstschmr can be helpful in removing any uncontrollable and unobservable modes.

See Also
minreal, obalreal, ohklmr, bstschmr, schmr, ss2tf, tf2ss

References
[1] T. Kailath, Linear Systems, Prentice-Hall, 1980, pp. 346-349.

stabproj, slowfast tree, istree