Extrapolation based interval approach to compute the frequency responses of non-rational transfer functions with nonlinear parametric dependencies

We consider the problem of computing the frequency response of a non-rational transfer function having uncertainties in the parameters. A complete characterization of the frequency plots of such a transfer function is provided and an efficient and guaranteed algorithm for computing the envelope of the Bode plot using interval analysis (IA) is devised. In particular, it is shown that the range enclosure property of the interval analysis can be used to compute the Bode envelopes of the non-rational transfer function with parametric dependencies. The range enclosures computed using IA are guaranteed to contain the minima and maxima of the function over a given box. The IA is combined with uniform subdivision technique to obtain the range enclosures of desired accuracy. We also show, how the well known Richardson extrapolation technique helps in accelerating the convergence process of the algorithm.