Exponential stabilization for 1-D linear Itô-type state-dependent stochastic parabolic PDE systems via static output feedback

Abstract

This paper deals with the problem of exponential stabilization for 1-D linear stochastic parabolic partial differential equation (PDE) systems with state-multiplicative noise in the form of Itô type. A static output feedback (SOF) control scheme is proposed to stabilize the stochastic PDE system in a stochastic framework via locally collocated piecewise uniform actuators and sensors. The closed-loop well-posedness analysis is provided by virtue of the semi-group theory. Based on the infinite-dimensional infinitesimal operator and Lyapunov technique, the SOF controller design is developed to guarantee the exponential stability of the resulting closed-loop system in the mean square sense. Finally, simulation results on a stochastic heat equation are presented to verify the effectiveness of the proposed design method.