On sample-based functional observability of linear systems

TL;DR

This paper explores the conditions under which a linear system's internal state functions can be reconstructed from limited, irregular output samples, extending the concept of sample-based observability.

Contribution

It introduces necessary and sufficient conditions for sample-based functional observability and analyzes sampling schemes to ensure these conditions are met.

Findings

Derived conditions for sample-based functional observability.

Established criteria for sampling schemes to guarantee observability.

Demonstrated applicability through a numerical example.

Abstract

Sample-based observability characterizes the ability to reconstruct the internal state of a dynamical system by using limited output information, i.e., when measurements are only infrequently and/or irregularly available. In this work, we investigate the concept of functional observability, which refers to the ability to infer a function of the system state from the outputs, within a samplebased framework. Here, we give necessary and sufficient conditions for a system to be sample-based functionally observable, and formulate conditions on the sampling schemes such that these are satisfied. Furthermore, we provide a numerical example, where we demonstrate the applicability of the obtained results.