Talk:Realization (systems)

Re Grey box completion and validation
See also“ “Grey box completion and validation“ has been removed anonymously without explanation from this and several other topics. Following advice from Wikipedia if there are no objections (please provide your name and reasons), I plan to reinstate the reference in a weeks time.

The removed reference provides additional techniques of potential interest to those working with the models of the type described. In particular most models are incomplete (i.e. a grey box) and thus need completion and validation. This reference seems to be within the appropriate content of the “See also” section see Wikipedia:Manual_of_Style/Layout#See_also_section.

BillWhiten (talk) 05:17, 22 March 2015 (UTC)

General System and Weighting Pattern: text incomplete or in error?
In the article I read:

"If we have an input $$u(t)$$, an output $$y(t)$$, and a weighting pattern $$T(t,\sigma)$$ then a realization is any triple of matrices $$[A(t),B(t),C(t)]$$ such that $$T(t,\sigma) = C(t) \phi(t,\sigma) B(\sigma)$$ where $$\phi$$ is the state-transition matrix associated with the realization."

Here the matrix $$A(t)$$ does not return in the condition $$T(t,\sigma) = C(t) \phi(t,\sigma) B(\sigma)$$, which seems odd.

After consulting https://en.wikipedia.org/wiki/Weighting_pattern, I suspect that this condition should read:

$$T(t,\sigma) = C(t) e^{A(t-\sigma)} B(\sigma)$$

Any objections?Redav (talk) 11:52, 22 June 2020 (UTC)


 * $$T(t,\sigma) = C(t) e^{A(t-\sigma)} B(\sigma)$$ is for linear time-invariant systems. $$T(t,\sigma) = C(t) \phi(t,\sigma) B(\sigma)$$ is the general case including time-variant systems, and $$\phi(t,\sigma)$$ depends on $$A(t)$$ (despite it not showing up in the notation). If you found this confusing, you could change $$ \phi(t,\sigma) $$ to $$ \phi_{A}(t,\sigma) $$, which is also custom in some books on linear systems. Saung Tadashi (talk) 12:00, 22 June 2020 (UTC)