Exponential stability of time-varying linear discrete systems

We are concerned with the stability of non-autonomous linear discrete-time systems. Two necessary and sufficient conditions are derived for exponential stability of time-varying linear discrete-time systems. They show that through a nonsingular state transformation an exponentially stable system can be reduced to a simple one with the coefficient matrix whose spectral norm being less than unity. Furthermore, an estimation of solution of time-varying linear discrete-time system is provided which extends the results in the literature.