MATH319 Slides

161 Criterion for well posed S⁢F⁢L

Lemma

The S⁢F⁢L system is well posed if and only if 1+G⁢K≠0, and in this case, the inputs determine the states by

[xyz]=11+G⁢K⁢[1-G-1K1-KG⁢KG1]⁢[rdn].

We abbreviate this to X=Φ⁢U. The proof consists of calculating the inverse of the matrix above.