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The purpose of this paper is to present a proportional-integral (PI) observer design on a linear system with stochastic noises.

The noised disturbances are modeled as independent Brownian motions for various affections, such as radiation, heat, and material fatigue. These phenomena are common in applications, such as biomolecules, nonlinear control, and biochemical networks. Under this framework, this paper proposes a new approach on a PI observer in terms of four crucial theorems, and an illustrative numerical example is given to verify the proposed design.

The results provide potential solutions for system fault tolerance and isolation.

This paper proposes a design, solvability, and controllability analysis on a PI observer in terms of four crucial theorems.