Global observer for Lotka–Volterra systems

Abstract

This paper develops a new approach to the long-standing problem of global asymptotic positive observer design for n -dimensional Lotka–Volterra (LV) systems. In this approach, instead of the state error dynamics, the notion of state ratio dynamics is used by exploiting the positivity property of the LV systems. A novel class of observers is proposed and the global asymptotic convergence of such observers is studied via a well-known logarithmic Lyapunov function. The obtained convergence conditions of the proposed observer are formulated as a linear matrix inequality (LMI), which can be used to determine the unknown parameters of the observer. This design procedure is modified for state estimation of time-varying LV systems, too. The applicability of the proposed method is investigated through two numerical examples.