Necessary and Sufficient Conditions for Distinguishability of Linear Control Systems

TL;DR

This paper presents a new, easier-to-verify condition for determining when two linear control systems are distinguishable, which is important for understanding system observability in hybrid systems.

Contribution

It introduces a simplified equivalent condition for distinguishability of linear systems, improving upon previous complex criteria.

Findings

New equivalent condition for distinguishability

Condition is easier to verify than previous criteria

Enhances analysis of hybrid system observability

Abstract

Distinguishability takes a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of linear systems. However, the condition is not easy enough to verify. This paper will give a new equivalent condition which is relatively easy to verify.