Detectability And Stability For Nonlinear Time-varying Discrete-time Stochastic System

This paper aims to study weak zero-state detectability and the uniform global asymptotic mean square stability for nonlinear time-varying discrete-time stochastic systems. Firstly, it prove that the zero-state detection is equivalent to the global asymptotical stability of the system, it is global mean square stabilitie. Then, this paper discusses uniform global asymptotic mean square stability for Reduced Limit Systems, and a new criterion is given to receive the stability of Reduced Limit Systems. Lastly, with the results of the paper discusses uniform global asymptotic mean square stability for the time-varying discrete stochastic cascade system.