Positive Observers Revisited

TL;DR

This paper demonstrates how positive linear systems can be stabilized with positive Luenberger-type observers, expanding the class of systems and conditions for convergence, including stochastic noise scenarios.

Contribution

It introduces a novel observer design that uses monotonic bounds for stabilization and extends the approach to nonpositive systems with stochastic noise.

Findings

Positive observers can stabilize linear systems with larger classes of dynamics.

Conditions for convergence are established for systems with stochastic noise.

The approach generalizes previous observer designs by incorporating positivity constraints.

Abstract

The paper shows that positive linear systems can be stabilized using positive Luenberger-type observers. This is achieved by structuring the observer as monotonically converging upper and lower bounds on the state. Analysis of the closed-loop properties under linear observer feedback gives conditions that cover a larger class than previous observer designs. The results are applied to nonpositive systems by enforcing positivity of the dynamics using feedback from the upper bound observer. The setting is expanded to include stochastic noise, giving conditions for convergence in expectation using feedback from positive observers.