Hi Vadim, Thanks for your feedback...

On 11/11/2013 9:52 PM, Vadim Zavalishin wrote: [snip on the analog stuff] >

For the discrete-time case the situation is more complicated, because we can't use the continuity of the state vector function. IIRC, I also didn't manage to build the "worst-case" signal, but there was the same problem of the state vector becoming larger in the absence of the input signal.

Interesting

That's why I was somewhat surprised that you simply managed to restrict the eigenvalues of the system matrix in some coordinates.

`To be clear: the eigenvalues of the transition matrix only cover`

`time-invariant stability.`

`The constraint for time-varying BIBO stability is that all transition`

`matrices P satisfy ||TPT^-1|| < 1 where ||.|| is the spectral norm and T`

`is some constant non-singular change of base matrix.`

`The main reason I am suspicious is that Laroche does not even try to`

`cook up a change of basis matrix, or to show when it might be achieved.`

`It's kind of an orphan result in that paper that goes unused for showing`

`BIBO stability.`

Particularly suspicious is that your coordinate transformation matrix is "built for the smallest damping", while the more problematic case seems to occur "at the larger damping".

`I'm not sure I follow you here. Smallest damping means most resonance,`

`where the system decays most slowly. Don't you think this would be where`

`the greatest problems would arise?`

> But, as I said, I didn't finish that

research and I could have been wrong. So just take my input FWIW.

`I have made a slightly cleaner cook-up of the change of basis matrix.`

`This seems a lot like the "uniformly negative" criteria you mentioned.`

`It could be read that k must be uniformly positive:`

http://www.rossbencina.com/static/junk/2x2ChangedBasisNorm.html In short, using change of basis matrix T: [1 f] [0 1] We have the time-varying BIBO stability constraint: 0 < f < 2, g > 0, f < k <= 2 f provides the bound on k from below. Ross. -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp