Contraction-based design of positive observers

Abstract

We consider the problem of positive observer design for positive systems. We propose the design of a nonlinear positive observer based on the use of generalized polar coordinates in the positive orthant. The contraction properties of the estimation error are studied thanks to the Hilbert projective metric. The optimization problem of finding the observer gains that maximize the contraction rate is addressed, and the simple two-dimensional case is discussed in detail.