The Grassmannian Manifold and Controllability of the Linear Time-Invariant Control Systems
The idea discussed here are mainly to develope some interesting
relationship between the differential geometry of certain curves and
the controllability of linear time-invariant (LTI) control systems
without considering any matrix riccati equation. The problem based on the basic concepts of controllability is
considered here. The two point boundary value problem (TPBVP)
is described here as a flow in the Grassmannian manifold. Then a
simple solution to determine a control function in the Grassmannian
manifold is presented that transfer the system states from initial to
final values and satisfies the conditions that are equivalent to the
controllability of the systems.
Keywords: Linear system, Control function, controllability,
Grassmannian manifold
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