Partial state and input observability recovering by additional sensor implementation: a graph–theoretic approach

Abstract

This article deals with the problem of additional sensor location in order to recover the observability of any given part of the state and unknown input for structured linear systems. The proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system's structure. We first provide graphical and necessary sufficient conditions for the generic observability of any given part of the state and input. Then, we study the number and location of additional sensors in order to satisfy the latter conditions. On the one hand, we provide necessary requirements to be satisfied by these additional sensors. On the other hand, we give other sufficient simple conditions allowing us to add a number, which is guaranteed to be minimal, of sensors to ensure the observability of any given part of the state and unknown input.

Keywords:

• partial state and input generic observability
• sensor location
• structured linear systems
• graph theory