Robust Filter for Linear Stochastic Partial Differential Systems via a Set of Sensor Measurements

This study addresses a robust H_∞ filtering design problem for linear stochastic partial differential systems (LSPDSs) with external disturbance and measurement noise in the spatio-temporal domain. For LSPDSs, the robust H_∞ filter design via a set of sensor measurements needs to solve a complex Hamilton Jacobi integral inequality (HJII) for robust state estimation despite external disturbance and measurement noise. In order to simplify the design procedure, a stochastic spatial state space model is developed to represent the stochastic partial differential system via the semi-discretization finite difference scheme and the Kronecker product. Then based on this model a robust H_∞ filter design is proposed to achieve the robust state estimation via solving the linear matrix inequality (LMI). The proposed robust H_∞ filter has an efficient ability to attenuate the effect of spatio-temporal external disturbance and measurement noise on the state estimation of LSPDSs from the area energy point of view. Finally, a robust H_∞ state estimation example is given for the illustration of design procedure and the performance confirmation of the proposed robust filter design method.