On the asymptotic stability of ARMA systems with mean square stable outputs with applications to adaptive control

Stochastic adaptive stabilization usually leads to the boundedness of the average of squared output of the stabilized system, but gives no conclusion on stability of the resulting system. The paper proves that an ARMA system is asymptotically stable if it is with mean sequence stable outputs. Thus, the adaptively stabilized stochastic system in its steady state is asymptotically stable-in the conventional sense