Observability and controllability analysis of linear systems subject to data losses

TL;DR

This paper develops verifiable conditions for key system properties like observability and controllability in discrete-time linear systems experiencing data losses, applicable to wireless and embedded networks with known loss patterns.

Contribution

It introduces an algorithm to decide observability and related properties for systems with data losses modeled by automata, linking these properties through established relations.

Findings

Provides necessary and sufficient conditions for system properties.

Develops an algorithm for deciding observability and controllability.

Analyzes the relation between data loss models and delay models.

Abstract

We provide algorithmically verifiable necessary and sufficient conditions for fundamental system theoretic properties of discrete time linear systems subject to data losses. More precisely, the systems in our modeling framework are subject to disruptions (data losses) in the feedback loop, where the set of possible data loss sequences is captured by an automaton. As such, the results are applicable in the context of shared (wireless) communication networks and/or embedded architectures where some information on the data loss behaviour is available a priori. We propose an algorithm for deciding observability (or the absence of it) for such systems, and show how this algorithm can be used also to decide other properties including constructibility, controllability, reachability, null-controllability, detectability and stabilizability by means of relations that we establish among these properties. The main apparatus for our analysis is the celebrated Skolem Theorem from linear algebra. Moreover, we study the relation between the model adopted in this paper and a previously introduced model where, instead of allowing dropouts in the feedback loop, one allows for time varying delays.