Robust stabilizability for a class of transfer functions

This paper is concerned with the robust stabilizability for single-input single-output plants. Robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency-dependent uncertainty band function around the transfer function of a nominal model. A necessary and sufficient condition for robust stabilizability is derived based on the well-known Nevanlinna-Pick theory in classical analysis. It is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model, in order for the class to be robustly stabilizable. A procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown.