Monitoring in a predator–prey systems via a class of high order observer design

Control of Lotka-Volterra Three Species System via a High Gain Observer Design

“…As is it well known, the Lotka-Volterra model describes interactions between several species in an ecosystem, predators and preys [5], we considered three equations, one describes the variations of the predator population, the two others equations describe the prey population.…”

“…Firstly, we give necessary and sufficient conditions to establish whether the system (3) is observable. Now, consider the following assumptions [5]:…”

“…In 1963, Lorenz first observed the chaos phenomenon in weather models. Since then, a large number of chaos phenomena and chaos behaviour have been discovered in physical, social, economical, biological and electrical systems [5]. Knowing the state system is necessary to solve many control theory problems, for example, stabilizing a system using state feedback [7].…”

Observer normal forms for a class of Predator–Prey models

“…Indeed, as far as we know, existing methods related to the synthesis of observers for Predator-Prey systems are basically based on the Luenberger observer applied to the linear part using the Lipschitz structure of these systems (see, e.g., [16,17,25,26] and references therein). There also exist other methods using high order polynomial observers [19] and interval observers [2,22]. Let us notice that most of these methods are based on the theorem given in [24], where an observer is designed around a stable equilibrium point.…”

Nonlinear Observer Normal Forms for Some Predator-Prey Models

“…If the above partial differential inequalities are positive, it is said that the populations i and j are in cooperation. To our knowledge, research that relate to the synthesis of observers for predator prey models are all based on the Leunberger's observer applied to the linear part using the Lipschitz structure of those models (López et al [2007a], Vaidyanathan [2010], López et al [2007b], Varga et al [2010] and references therein), works using high order polynomial observer Mata-Machuca et al [2010], or interval observer Bernard et al [1998], Rapaport and Harmand [2002]. In this work, we propose to develop nonlinear observer normal forms for some prey-predator models.…”