Stochastic Stability of Some Classes of Nonlinear 2D Systems

Abstract

The paper considers nonlinear discrete and differential stochastic repetitive processes using the state-space model setting. These processes are a special case of 2D systems that originate from the modeling of physical processes. Using the 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 exponential passivity in the second moment is used, together with the vector storage function, to develop a new method for output feedback control law design. An example of a system with nonlinear actuator dynamics and state-dependent noise is given to demonstrate the effectiveness of the new results.