True worst-case analysis of linear electrical circuits by interval arithmetic

Interval arithmetic can be used for computation of the range of a function when the domain is an
m
-dimensional box. In other words, interval arithmetic provides a method for performing global optimization over a simple domain. The network function of a linear network can be written in a multilinear form where some or all of the component values appear as variables. For a given frequency it is thus possible to compute the range of the network function over the intervals of the selected component values. Dependence on a common parameter such as temperature can also be modeled. By interval arithmetic a true worst-case analysis with sharp bounds can be performed. The interval result quoted above can be obtained with a method detecting intervals of monotonicity by interval computation of the partial derivatives. If the network function is not monotone over the whole domain, a partitioning technique is used to obtain intervals with monotonicity. The method is demonstrated on two examples.