The controllability decomposition reveals the inner structure and the reachable subspace of the system. The subspace can be visualized for second- and third-order systems and in general is a manifold.
An affine system. »
Its reachable subspace is a sphere.
The transformation reveals that it is confined to a specific sphere because .
The system starts and remains on the same sphere for all inputs.
TryBuyMathematica 12.3 is availableon Windows, macOS, Linux & Cloud. »
Questions? Comments? Contact a Wolfram expert »