LINEAR MULTICHANNEL CONTROL: A SYSTEM MATRIX APPROACH

A Bülent Özgüler

Prentice Hall International Series in Systems and Control Engineering

ISBN 0-13-155558-8 (hbk)

Disturbance Decoupling Problem
Regulator Problem
Decentralized Stabilization Problem
Noninteracting Control Problem
Almost Decoupling and Noninteracting Control

In each problem the internal stability of the feedback loop is a further requirement. In every case it encompasses a number of more specialized problems that seem unrelated at first glance. For instance, the regulator problem is a generalization of tracking, rejection of disturbances generated by known dynamics, frequency response approximation, and deadbeat control problems. All problems are typically multichannel, in that one channel of the plant is reserved for the controller that is required to achieve various objectives on the remaining channels. The above problems are collected and treated in a common framework which again uncovers some interrelations. For instance, the decentralized stabilization problem is viewed as a second channel canonicity problem which ties it nicely with the disturbance decoupling and the regulator problems.

The solvability conditions are stated in terms of system matrices associated with the open-loop plant so that the relevance of the open-loop poles and zeros to solvability is immediately readable from the given conditions. Since stability is a major issue in all problems and due to many conceptual simplifications it provides, the tool of stable proper fractions (or factorizations) is used in deriving these conditions. In this approach, the linear matrix equations over the ring of stable proper rational functions play an intermediary role and the book also contains many less familiar facts on these.

Some highlights from the main results are as follows:

* A characterization of the set of all solutions to the regulator problem is obtained in terms of the set of all solutions to a linear matrix equation in terms of system matrices. Exact conditions under which a linear fractional parametrization of solutions is possible are given.

* The set of all solutions to decentralized stabilization problem is described in a manner which makes the identification of the set of "unadmissible controllers" easy. The role played by the assumption of "strong-connectedness" in the set of all dynamic solutions is clarified.

* The main differences between the solvability conditions for the exact and the almost disturbance decoupling problems are indicated in terms of the open loop invariant zeros of the plant.