Partial Causal Detectability of Linear Descriptor Systems and Existence of Functional ODE Estimators

TL;DR

This paper introduces the concept of partial causal detectability for linear descriptor systems, providing a rank-based criterion and establishing its equivalence to the existence of functional ODE estimators, supported by a numerical example.

Contribution

It defines partial causal detectability for descriptor systems and links it to the existence of functional ODE estimators, offering new theoretical insights.

Findings

Partial causal detectability characterized by a rank criterion.

Equivalence between partial causal detectability and functional ODE estimators.

Numerical example validates the theoretical results.

Abstract

This paper studies the problem of state estimation for linear time-invariant descriptor systems in their most general form. The estimator is a system of ordinary differential equations (ODEs). We introduce the notion of partial causal detectability and characterize this concept by means of a simple rank criterion involving the system coefficient matrices. Also, several equivalent characterizations for partial causal detectability are established. In addition, we prove that partial causal detectability is equivalent to the existence of functional ODE estimators. A numerical example is given to validate the theoretical results.