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[edit] Controllability vs Reachability

What historically has been named 'controllability' is ambiguous. Let x₀ be the equilibrium state (usually taken to be 0) of a system in the absence of an input then.

1. Reachability of an arbitrary state, x_f, from an arbitrary state x_i is the ability to transfer from the initial state x_i to the final state x_f in some time by applying a suitable input.
2. Controllability of an arbitrary state, x, is the ability to transfer from this state x to the equilibrium state x₀ in some time by applying a suitable input.

Obviously reachability implies controllability. For linear stystems in continuous time, both concepts are equivalent. However, a discrete time system my be controllable without being reachabable. A trivial example is:

where A is nilpotent.

Mastlab 21:29, 10 September 2006 (UTC)

Removed the line referring to not being able to stay in a state once you've reached it, because the ability to stay in a state is implied in the ability to reach any state (including the one you're in) from here. What a state I'm in. —Preceding unsigned comment added by 76.64.141.149 (talk) 03:17, 27 November 2008 (UTC)

[edit] Page needs attention/improvement

A,B are matrices, but they are treated as vectors. For example, see "n columns of C ", "B and AB are independent and span the entire plan", etc. --kris (talk) 08:00, 1 June 2009 (UTC)

See recent changes. I think dimensionality is now properly handled for the most general case.—TedPavlic (talk) 12:17, 2 June 2009 (UTC)