Added basic implementation of compreal for state space realization

[JD123473]

Summary

Based on the MATLAB implementation, this function returns the state space realization to observable or canonical companion form, as well as the transformation matrix T.

Implementation

• Controllable form: T = ctrb(A, B)
• Observable form: T = inv(obsv(A, C))

Testing

• Tests added via %!test and %!error blocks
• Covers: TF equivalence, correct T matrix, invalid realization error

Reference

T. Kailath, Linear Systems. Prentice-Hall, 1980. ISBN 0-13-536961-4

• eq(15a) and eq(15b)

[ttl-octave]

Thank you very much for the contribution. I have some comments regarding parameter check (in order to prevent misleading error messages).

And what do you mean by "Based on the MATLAB implementation"? Please note that the code that you provide is completely yours and must not, under no circumstances, be somehow based on any MATLAB code.

[ttl-octave]

I guess "statistics package" is a copy & paste artifact? ;-)

[ttl-octave]

Please check the parameters before using them, otherwise the error message might be misleadig for the user. As far as I can see:

• First arg must be a SISO LTI system
• Second must be a string, where the default is 'c' if it is omitted
• It would also be helpful to check for controllability or observability resp. before computing the transformaiton in order to prevent ambiguous error messages

[ttl-octave]

Space between function name and argument list. Indentation within if-else-block

[ttl-octave]

In case of a non observable system, inverting the observability matrix in line 105 already fails (either because matrix is not invertible or because matrix is not square (MIMO)).