# Mixed $H_-/H_{\infty}$ Fault Detection Filtering for It\^o-Type Affine Nonlinear Stochastic Systems

## TL;DR

This paper develops new $H_-/H_{ ext{infty}}$ fault detection filters for Itô-type nonlinear stochastic systems, balancing robustness and sensitivity, with criteria based on Hamilton-Jacobi inequalities and linear matrix inequalities.

## Contribution

It introduces sufficient conditions for the existence of mixed $H_-/H_{ ext{infty}}$ filters for nonlinear stochastic systems using HJIs and LMIs, advancing fault detection methods.

## Key findings

- Derived criteria for filter existence using HJIs.
- Provided LMI-based conditions for quasi-linear systems.
- Numerical example demonstrating filter effectiveness.

## Abstract

This paper studies the mixed $H_-/H_{\infty}$ fault detection filtering of It\^o-type nonlinear stochastic systems. Mixed $H_-/H_{\infty}$ filtering combines the system robustness to the external disturbance and the sensitivity to the fault of the residual signal. Firstly, for It\^o-type affine nonlinear stochastic systems, some sufficient criteria are obtained for the existence of $H_-/H_{\infty}$ filter in terms of Hamilton-Jacobi inequalities (HJIs). Secondly, for a class of quasi-linear It\^o systems, a sufficient condition is given for the existence of $H_-/H_{\infty}$ filter by means of linear matrix inequalities (LMIs). Finally, a numerical example is presented to illustrate the effectiveness of the proposed results.