On Functional Estimator Design for Linear Discrete-Time Descriptor Systems

This paper addresses the problem of designing functional estimators for linear discrete-time descriptor systems. Unlike full-state estimators, functional estimators are preferred as they directly estimate specific linear combinations of system states without requiring the estimation of the entire state vector. This work presents a new set of sufficient conditions for the existence of functional estimators for discrete-time descriptor systems, expressed in terms of a rank condition and a linear matrix inequality formulation. The effectiveness of the proposed approach is demonstrated through its application to estimating the state of charge of a lithium-ion battery. An academic example is also provided to show that the obtained conditions are less restrictive than those in the existing literature on functional estimators for linear discrete-time descriptor systems.