Observer design of positive quadratic systems

Abstract

Our previous study has proposed a positive quadratic system representation for molecular interaction in a cell, including a signal transduction pathway and gene regulatory network, and also has presented a method for finding a positive invariant set depending on the initial state. Furthermore, we have shown that every positive rational system, which is used as a mathematical model expressing biological behavior, can be approximately represented by a singular perturbed positive quadratic system. This paper continues upon this research and proposes a new observer for such positive quadratic systems, called a positive quadratic system observer. We derive a sufficient condition on the observer for the estimation error to converge to zero as time goes to infinity for all initial estimation errors.