Polynomial Matrix Approach

Abstract

In contrast to the preceding chapter where a state space model of the plant and state feedback controller are exclusively utilized for decoupling problem, we will employ unity output feedback compensation to decouple the plant in this chapter. Polynomial matrix fractions as an input-output representation of the plant appear a natural and effective approach to dealing with output feedback decoupling problem. The resulting output feedback controller can be directly implemented without any need to construct a state estimator. In particular, we will formulate a general decoupling problem and give some preliminary results in Section 1. We start our journey with the diagonal decoupling problem for square plants in Section 2 and then extend the results to the general block decoupling case for possible non-square plants in Section 3. A unified and independent solution is also presented in Section 4. In all the cases, stability is included in the discussion. A necessary and sufficient condition for solvability of the given problem is first given, and the set of all compensators solving the problem is then characterized. Performance limitations of decoupled systems are compared with a synthesis without decoupling. Numerous examples are presented to illustrate the relevant concepts and results.