Positive Unknown Input Observer For Positive Linear Systems

TL;DR

This paper introduces a novel method for designing positive unknown input observers for positive linear systems, addressing the challenge of estimating states in the presence of unknown inputs while maintaining positivity constraints.

Contribution

It proposes a new design procedure for positive unknown input observers using LMIs and positivity conditions, filling a gap in observer design for positive systems with unknown disturbances.

Findings

Successful design of PUIOs using LMI-based stabilization

Ensured positivity constraints in observer parameters

Applicable to positive linear systems with unknown inputs

Abstract

Positive systems are important class of dynamic systems with impressive properties. The response of such systems to positive initial conditions and positive inputs remain in the nonnegative orthant of the state space. Although positive observers have been designed for positive systems, they are unable to estimate the states when unknown inputs or disturbances are present in the systems. This paper is a first attempt to design positive unknown input observers (PUIO) for positive linear systems. The structural constraints on observer parameters make the design task cumbersome. However, with the aid of a positive stabilization scheme via LMI and by imposing conditions on positivity of the generalized inverse associated with a certain design matrix, we provide a reliable procedure for the design of PUIOs.