On Notions of Output Finite-Time Stability

Lyapunov characterizations of output finite-time stability are presented for the system ẋ = f(x), y = h(x) which is locally Lipschitz continuous out of the set Y = {x ∈ℝ
ⁿ
: h(x) = 0} and continuous on ℝ
ⁿ
. The definitions are given in the form of K and KL functions. Necessary and sufficient conditions for output finite-time stability are given using Lyapunov functions. The theoretical results are supported by numerical examples.