I think it might be helpful to post a script of the textbook question from 3.7.6. (i) and (ii) are assumptions of the model and there are subquestions from a) to k). The parts I need some help are g) to k). I would appreciate any help!
Sorry about the typo. You're right. It should be $$\dot z = ly$$. And as I said in the relevant equations, ##u## is only linearly dependent on ##z##, and it should have no dimension. ##a##,##b## are constants without dimensions which depends on constants ##k##,##l## and ##x_0##.(##x_0##=##x(0)##...
For g) how should I argue this claim? To me it seems straight forward because u is linearly related to z. Then so do their derivatives. And by the description of the model, ##\dot z## is linear to y. So it's quite obvious but not sure what I should pay more attention to when I write my proof...