Robust stabilizability for a class of transfer functions

This paper is concerned with the robust stabilizability for single-input single-output systems. The robust stabilizability means that all the transfer functions in the given class, characterized by the nominal plant model and the uncertainty band function, can be stabilized simultaneously by a fixed controller. A necessary and sufficient condition for robust stabilizability is derived based on a classical result in the interpolation theory of bounded real functions. It is shown that the magnitude of the uncertainty band function should be restricted within a certain range in order that the class is robustly stabilizable. An extension of the result to the servo problem is also discussed.