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# 7.9 Other Models of Time-Varying Delays

In this section, models of time-varying delays which are not linearly or quadratically time variant are briefly considered.

## 7.9.1 Taylor Series Expansion of Range and Delay

The time-varying range R(t) can be expanded in Taylor series, around t0, with Lagrange residual term:

(7.370)

where R(n)(·) denotes the nth-order derivative of R(·), and if t > t0 and if t < t0. This expression can be substituted into (c07-mdis-0044) to get an n-order algebric equation in D(t). One of the roots of this equation is the time-varying delay D(t) for the given R(t) (see Section 7.4 for the case n = 2 and ).

Alternatively, by following the approach in (Kelly 1961) and (Kelly and Wishner 1965), the time-varying delay D(t) can be expanded in Taylor series, around t0, with Lagrange residual term:

(7.371)

where if t > t0 and if t < t0.

This approach, when is embedded ...

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