Interval reduced-order switched positive observers for uncertain switched positive linear systems

TL;DR

This paper develops conditions and methods for designing reduced-order positive observers for uncertain switched positive linear systems, enabling effective state estimation despite switching and uncertainties.

Contribution

It introduces a novel design procedure for reduced-order positive observers applicable to both switched and non-switched uncertain positive linear systems.

Findings

Observers of order (n - p) are successfully designed.

The approach handles arbitrary switching and uncertainties.

Numerical examples validate the theoretical results.

Abstract

In this paper, existence conditions and a design procedure of reduced-order switched positive observers for continuous- and discrete-time switched positive linear systems with uncertainty are established. In the analyzed class, arbitrary switching is permitted, whereas the uncertainty expressed via matrix inequalities concerns both the initial state and system parameters. Positive lower and positive upper interval switched observers are obtained. The proposed observers are of (n - p) order, where n is the dimension of the state vector and p is the rank of the output matrix, i.e., p-dimensional measurement information. Moreover, as a special case, existence conditions and a design procedure of reduced-order positive observers for uncertain positive linear systems without switching are provided. The theoretical findings are illustrated by two numerical examples for continuous- and discrete-time systems.