Existence Conditions for Functional ODE Observer Design of Descriptor Systems Revisited

TL;DR

This paper revisits the conditions for designing functional ODE observers for descriptor systems, offering new algebraic criteria that are easier to verify and implement, with demonstrated numerical examples.

Contribution

It introduces milder, purely algebraic existence conditions for functional ODE observers in descriptor systems, expanding upon previous results.

Findings

New algebraic existence conditions for observers

Observer order is less than or equal to the estimated functional vector

Design algorithm demonstrated with numerical examples

Abstract

This paper is devoted to the problem of designing functional observers for linear time-invariant (LTI) descriptor systems. The observers are realized by using state-space systems governed by ordinary differential equations (ODEs). Available existence results for functional ODE observers in the literature are extended by introducing new and milder sufficient conditions. These conditions are purely algebraic and provided directly in terms of the system coefficient matrices. The proposed observer has an order less than or equal to the dimension of the functional vector to be estimated. The observer parameter matrices are obtained by using simple matrix theory, and the design algorithm is illustrated by numerical examples.