System theory on group manifolds and coset spaces

摘要

Controllability, observability, and realization theory are studied for a particular class of systems for which the state space is a differentiable manifold which is simultaneously a group or, more generally, a coset space. It is possible to give rather explicit expressions for the reachable set and the set of indistinguishable states in the case of autonomous systems. A type of state space isomorphism theorem is established. These results parallel, and in part specialize to, results available for the familiar case described by the differential of x(t) = Ax(t) Bu(t); y(t) = Cx(t). The objective is to reduce all questions about the system to questions about Lie algebras generated from the coefficient matrices entering in the description of the system and in that way arrive at conditions which are easily visualized and tested.