Nonuniform complete observability; preservation by output feedback and duality results

TL;DR

This paper introduces a new nonuniform complete observability property for nonautonomous linear systems, demonstrating its preservation through output feedback and establishing a duality with controllability.

Contribution

It defines nonuniform complete observability, proves its preservation under output feedback, and establishes duality with nonuniform complete controllability.

Findings

Nonuniform complete observability is more general than uniform complete observability.

Preservation of nonuniform complete observability via output feedback.

Duality between nonuniform complete observability and controllability.

Abstract

In this paper we propose a new observability property for nonautonomous linear control systems in finite dimension; the nonuniform complete observability, which is more general than the uniform complete observability. The main result of this work will prove that nonuniform complete observability is preserved via output feedback. In addition, the duality between this concept and the recently introduced concept of nonuniform complete controllability will be proved, leading to the result of preservation of nonuniform complete controllability via input feedback.