Stability and absence of overflow oscillations for 2-D discrete-time systems

In this correspondence, it is shown that a 2-D linear time-invariant discrete-time system could be bounded-input bounded-output (BIBO) unstable even if the 2-D system, which is implemented by finite word length, is free of overflow oscillations with zero input, according to a previous criterion for absence of overflow oscillations in 2-D discrete-time systems. An improved criterion is presented to ensure both stability properties.