A Fault Diagnosis Method Based on Zonotopes

Abstract. In this paper, zonotope theory is used to address the problem of detecting faults in technical systems described by discrete-time dynamic linear models with exogenous disturbances and measurement noise. To construct the corresponding zonotope, a reduced (lower-dimensional) model of the original system is developed; this model is insensitive to exogenous disturbances. To simplify the solution procedure, the matrices of the reduced model are written in the identification canonical form, which also ensures model stability. Based on this form, an equation is derived to find a solution of minimal dimension. If the insensitivity to exogenous disturbances cannot be achieved, a minimum sensitivity solution is obtained. Based on the resulting model, a diagnostic observer is designed that generates a residual for deciding on the presence/absence of faults. The observer design formulas are used to construct a fault-detecting zonotope. The theoretical framework is illustrated with a practical problem of detecting faults in an electric drive of an underwater vehicle as an example. According to the simulation results in MATLAB, the theoretical framework is correct.

Keywords: discrete systems, faults, diagnostic observers, residual, disturbances, measurement noise, zonotopes.

Acknowledgments. This work was supported by the Russian Science Foundation, project no. 25-19-00590, https://rscf.ru/project/25-19-00590/.

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Zhirabok, A.N., Zuev, A.V., and Protsenko, A.A., A Fault Diagnosis Method Based on Zonotopes. Control Sciences 3, 17–22 (2026).

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