Communications of the
Korean Mathematical Society CKMS

The purpose of this paper is to establish discrete versions of the well-known Lyapunov's stability theorem and LaSalle's invariance theorem for a non-autonomous discrete dynamical system. Our proofs for these theorems are constructive in the sense that they are made by explicitly building a Lyapunov function for the system. A comparison between non-autonomous discrete dynamical systems and continuous dynamical systems is conducted.

Keywords: non-autonomous discrete dynamical system, Lyapunov function, exponentially stable fixed point

MSC numbers: 37B55, 34D20, 37B25