Stability of stochastic repetitive processes

The paper considers nonlinear discrete and differential stochastic repetitive processes using the state-space model setting. These processes are a particular case of 2D systems that have their origins in the modeling of physical processes. Using a vector Lyapunov function method sufficient conditions for stability in the mean square are obtained in the stochastic setting, where the vast majority of the currently known results are for deterministic dynamics. Based on these results the property of stochastic dissipativity in the second moment is introduced and then a particular case of this property, termed exponential passivity in the second moment, is used, together with a vector storage function, to develop a new method for output feedback based control law design. An example of a system with nonlinear actuator dynamics and state-dependent noise is given to demonstrate effectiveness of the new results.