TABLE OF CONTENTS The objects under study in control theory are systems. A system is any set of elements connected together by information links within some delineated system boundaries.
Referring to Figure 1.1, note that the system boundary is not a physical boundary but rather a convenient fictional device. Note also how information links may pass through the system boundary.
Since control theory deals with structural properties, it requires system representations that have been stripped of all detail, until the main property that remains is that of connectedness. (The masterly map of the London Underground system is an everyday example of how useful a representation can be when it has been stripped of all properties except that of connectedness.)
Connectedness is a concept from topology. Topology, the discipline that studies the underlying structure of mathematics, offers fascinating reading to aspiring systems theorists. Recommended reading is given in the Bibliography. Clearly, a system is a very general concept; control theory is most interested in certain classes of system and to make progress we delineate the classes. First it is interested in dynamic systems - these are systems whose behaviour over a time period is of interest. Thus if a system were concerned with population aspects, a similar dynamic system would be concerned with population growth.
Secondly, it is most interested in and most powerful when dealing with linear systems. A linear system is characterised by the property shown in Figure 1.2. The upper...
