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In this paper, the design problem of simultaneous estimation of unmeasurable states and unknown inputs (UIs) is investigated for a class of discrete-time linear implicit models (DLIMs). The UIs affect both state and output of the system. The approach is based on the separation between dynamic and static relations in the considered DLDM. First, the method permitting to separate dynamic equations from static equations is exposed. Next, an augmented explicit model which contains the dynamic equations and the UIs is constructed. Then an unknown inputs observer (UIO) design in explicit structure is developed. The exponential convergence of the state estimation error is studied by using the Lyapunov theory and the stability condition is given in term of linear matrix inequality (LMI). Finally, an illustrative application of a heat exchanger pilot process is given to show the good performances of the proposed method.

State and Unknown Input Simultaneous Estimation for a Class of Discrete-Time Linear Implicit Models : A Heat Exchanger Pilot Process Application