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A Functional Unknown Input Observer for Linear Singular Fornasini–Marchesini First Model Systems: With Application to Fault Diagnosis

Estimation of the state variables of dynamical systems in the presence of noise, disturbance, and fault is an important problem in the control and monitoring field. In this article, the mentioned issue is addressed for singular 2-D systems in Fornasini–Marchesini first model (FM-I). In this regard, a functional unknown input observer is proposed to eliminate the effects of unknown inputs and estimate a given linear combination of the system states. Moreover, the proposed observer can be used to estimate the faults and necessary and sufficient conditions for the simultaneous estimation of states and faults are derived. Finally, the performance of the proposed estimation methods is validated through a numerical example and a second-order parabolic heat equation.