A DUAL LOOK AT UNIT INTERPOLATION IN H-INFINITY

Using mappings of the form (1 + bf)(a), (1 - bf)(-a) and ((1 + bf)/(1 - bf))(a), we get three different unit interpolation algorithms, respe ctively first, second and third. The second algorithm yields a unit in H infinity with arbitrary specified left half s-plane zeros instead o f arbitrary specified left half s-plane poles, as in Youla er al. (197 4) and Vidyasagar (1985) with the first algorithm. The third algorithm yields a unit in H infinity with considerably lower degree in the cas es where a is required to be greater than one with either the first or second algorithms judiciously, as shown by a numerical example, one c an reduce the second algorithm. However, by using alternative steps fr om the first and order of the unit considerably, compared with the use fulness of the second algorithm in the control system context is that the closed-loop system poles can be specified arbitrarily in the LHP i n a strong stabilization problem, which is the opposite to the first a lgorithm of Youla et the LHP in an arbitrary way. The second algorithm can also be used far placing the interconnected closed loop system po les in decentralized stabilization for expanding construction of large scale systems.