Observer normal form design for the nonlinear MIMO systems using coupled auxiliary dynamics

Abstract

This paper presents a transformation of a class of nonlinear multiple-input and multiple-output (MIMO) dynamical systems into a class of extended nonlinear normal forms. The extended normal forms are compatible with the widely used high-gain observer, which enables the estimation of the system’s states. It is realized by using a series of transformations which are performed by means of the so-called dynamics extension method, which explicitly supplies a set of auxiliary dynamics and a change of coordinates. Many researchers have focused their efforts on transforming nonlinear dynamical systems into normal forms of nonlinear observers. However, few of proposed transformations have been specifically developed for MIMO systems using an extended dynamics transformation. The main objective of this work is to fill this gap and provide a class of nonlinear dynamical systems that support the extended dynamics method, which can lead to a better understanding of their structures. Additionally, the results are highlighted by studying a class of nonlinear systems that describe the Dengue fever infection status of both human and mosquito populations. Finally, the effectiveness of the proposed high-gain observer is verified through a numerical example.