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

Abstract

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.

Discrete-time Takagi-Sugeno singular systems with unmeasurable decision variables: state and fault fuzzy observer design

“…Various studies has investigated the issues related to state and unknown input estimation [21][22][23], as well as state and faults estimation [24,25] and many approaches has been the objective of fuzzy observer design as in [21,24] when authors use the Lipschitz constraints. In other side other approach has been applied by authors in [23,25] based on the separation between dynamic and static relations in T-S singular model. A study has been treated in [26], aiming at the estimation of states, actuator, and sensor faults in nonlinear systems with a polytopic linear parameter varying representation.…”