Abstract
We consider the finite time input-to-state stability of autonomous discrete time systems, where the state enters a ball around the origin, with a radius determined by the input magnitude, in finite time. This extends the notion of classical input to state stability where this condition is only achieved asymptotically. We provide several types of Lyapunov functions that guarantee finite time input-to-state stability and characterize their equivalence. We also give converse Lyapunov theorems correcting a mistake in [1].
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