State-Linearization of Positive Nonlinear Systems; Applications to Lotka-Volterra Controlled Dynamics

Wiktor Malesza1,Witold Respondek2

1Institute of Control and Industrial Electronics, Warsaw University of Technology ul. Koszykowa 75 00-662 Warsaw, Poland wmalesza@isep.pw.edu.pl

2Laboratoire de Mathématique, INSA de Rouen Pl. Emile Blondel 76131 Mont Saint Aignan, France wresp@insa-rouen.fr

ABSTRACT. A notion of positive linear and positive nonlinear systems is introduced (as an intrinsic formalization of positive invariance). A characterization of positive linear and nonlinear smooth control systems is given. Necessary and sufficient conditions for local equivalence, under a change of coordinates, of positive nonlinear control systems to a positive linear system are established.

KEYWORDS: positive linear systems, positive nonlinear systems, state-linearization

1. Introduction

An inspiration to study positive invariant control systems follows from the theory of positive linear control systems which is well known and almost complete. By definition, positive systems are those whose all trajectories are entirely confined in the nonnegative orthant image for all instances t ≤ t0, for all initial conditions in image, and all controls taking values in . Positivity is a property of a number of ...

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