Robust Control Toolbox™

Slow and fast modes decomposition

Syntax

• [G1,G2] = slowfast(G,cut) 
  

Description

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

where

denotes the slow part of G(s), and

denotes the fast part. The variable cut denotes the index where the modes will be split.

stabproj employs the algorithm in [1] as follows:

Find a unitary matrix V via the ordered Schur decomposition routines blksch or rschur such that

Based on the style of ordered Schur form, you get .

Finally solving the matrix equation for X

you get the state-space projections

and

where

and

References

[1]  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.

See Also
schur       Schur decomposition

modreal     Modal form realization

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