Appendix 4

It is assumed that the transfer function in the *s*-domain for the solution of a linear differential equation can be written as follows:

$G(s)=\frac{K}{{s}^{n}}\xb7\frac{{S}_{1}\xb7{S}_{2}\cdots {S}_{k}\xb7{Q}_{1}\xb7{Q}_{2}\cdots {Q}_{l}}{{S}_{k+1}.{S}_{k+2}\dots {Q}_{l+1}\xb7{Q}_{l+1}\dots}$ (A4.1)

(A4.1)

for some *n*, l, *k*≥0, where *S*_{i} and *Q*_{j} are linear and quadratic expressions in *s*:

${S}_{i}=s\xb7{\tau}_{i}+1$ (A4.2)

(A4.2)

${Q}_{j}={\left(\frac{s}{{\omega}_{j}}\right)}^{2}+2\xb7{\zeta}_{j}\xb7\frac{s}{{\omega}_{j}}+1$ (A4.3)

(A4.3)

The parameters *τ*_{i}, *ω*_{j}, and *ζ*_{j} are all assumed positive. The functions (A4.2) and (A4.3) determine ...

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