Unit interpolation in H∞: Bounds of norm and degree of interpolants

This paper studies the problem of unit interpolation in H_∞. Specifically, bounds of the norm and degree of interpolants are obtained using the Nevanlinna-Pick interpolation theory. Also simpler bounds are given using the Poincaré metric. These results indicate that strong stabilization and simultaneous stabilization need a cautious approach if the system is ‘ill-conditioned’. In fact, it is demonstrated that the degree of stable compensator is not bounded for the class of plants with fixed degree. Also an example shows that there is a class of plants for which the sensitivity can be made small only if unstable compensators are used.