Minimality, controllability and observability for uncertain systems

A complete generalization of the notions of minimality, controllability and observability is presented for uncertain systems modelled by linear fractional transformations on structured operators. Both an algebraic perspective and a geometric perspective are given. The algebraic results include necessary and sufficient linear matrix inequality conditions for reducibility, and the development of structured controllability and observability matrices. The geometric approach involves a decomposition of the system variable space into reachable and unobservable subspaces. Both approaches lead to Kalman-like decomposition structures for uncertain systems.