## 1984

# Decentralized Control System Design: Dynamic Coupling from a Geometric Viewpoint

William H. Bennett

Doctoral Dissertation, Year: 1984, Advisor: John S. Baras

**Abstract**

This dissertation provides a new, frequency dependent, notion of dynamic weak coupling between subsystems which is useful for the design of decentralized control systems. An abstract geometric Nyquist criterion for multiloop systems is used to develop both a new measure of system stability margin and a new measure of subsystem weak coupling. The measure of stability margin developed has the advantage over standard measures of exposing certain additional internal stability properties of a feedback system. The weak coupling measure is useful to estimating stability properties (and therefore certain control system design objectives) of a decentralized control system and appears to be more generally applicable than other available measures of weak coupling.

The essential topological features of the abstract Nyquist criterion is employed in this dissertation involved near intersection between a certain pair of linear subspaces (parameterized by the complex frequency variable s) of the direct sum of all the system imputs and outputs. The measures employed are derived from the idea of the gap between subspaces. Computational methods are provided based on the idea of principal angles between a pair of linear subspaces.

A review of some well known methods for design of decentralized control systems using other notions of subsystem weak coupling is provided. Some examples are included which serve to illustrate the ideas and compare with other well known techniques.