Controllability and observability of uncertain linear time-invariant systems

The article [S 7 130] "Representation of a linear system. Extensions to uncertain systems" introduced state model representation, and showed how this model could be obtained from an initial representation in the form of a differential equation or transfer function, and how, for a complex system made up of interconnected subsystems, a global state model could be obtained that preserves structural information.

For the sake of simplicity, the fundamental –– notions of governability and observability had been omitted, so that the three types of representation (transfer function, differential equation, state model) could be assumed to correspond to the same knowledge of the system.

This is not always the case, and the state representation of a system may be of a higher order than the transfer function, or even the differential equation. Why do these modes exist? What are the consequences? These are two fundamental questions in theory, but also very important in practice, and we'll start by answering them in the absence of uncertainty. Secondly, we'll return to the case of uncertain linear systems, whose LFT representation was also discussed in the article [S 7 130] . We will study how the notion of governability generalizes to such systems.