Robust Control Toolbox™

Stable and antistable projection

Syntax

• [G1,G2,m] = stabproj(G) 
  

Description

stabproj computes the stable and antistable projections of a minimal realization G(s) such that

where

denotes the stable part of G(s), and

denotes the antistable part. The variable m returns the number of stable eigenvalues of A.

Algorithm

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 can get a stable and an antistable .; for the case of slowfast.

Finally solving the matrix equation for X

you get the state-space projections or

and or

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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