Stability Conditions for Discrete-Time Stochastic Systems Introduced on Left-Bounded Time Interval

Stability conditions for discrete-time stochastic systems characterized by general stochastic processes have been discussed in earlier articles, under the assumption that the systems are introduced on the unbounded time interval. This letter newly develops theoretical bridges between the frameworks of those stability conditions and the stochastic systems introduced on the left-bounded time interval, and explicitly shows necessary and sufficient stability conditions on the left-bounded time interval. The results in this letter are expected to be useful for ensuring the validity of the future developments of control theory on the unbounded time interval.