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consider the following transfer functions: $$ G(s)=\frac{1}{\tau s+1}G_0 \quad \tau_{min}<\tau<\tau_{max} $$ show that this system equal to model with additive perturbation as follow $$ G(s)=G_1(s)+W(s)\Delta \qquad ||\Delta||\le1 $$ $\Delta$ is perturbation and where $$ W(s)=-\frac{r_{\tau}\tau_ms}{(1+\tau_m s)^2}\qquad G_1(s)=\frac{G_0}{(1+\tau_m s)} $$ in this $$ \tau_m=\frac{\tau_{max}+\tau_{min}}{2}\quad r_{\tau}=\frac{\tau_{max}-\tau_{min}}{\tau_{max}+\tau_{min}} $$ and

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  • $\begingroup$ @AJN I edited the question. thank you for your attention $\endgroup$
    – u1997
    Nov 28 '21 at 5:38
  • $\begingroup$ Is there any assumption on $G_0$ ? Like its order or if it a proper transfer function etc. ? I think that there probly exists some assumption that order of $G_0$ denominator is one more than $G_0$ numerator. $\endgroup$
    – AJN
    Nov 28 '21 at 16:55
  • $\begingroup$ yes, $G_0$ is a proper transfer function. $\endgroup$
    – u1997
    Nov 28 '21 at 19:04

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