A direct method for the construction of nonlinear discrete-time observer with linearizable error dynamics

We provide a direct method for the design of nonlinear discrete-time observers by a construction of a change of variables. An explicit expression of the change of variables is given. Some simulations for chaotic systems, such as Lozi system and He/spl acute/non system, are provided to illustrate the proposed method.

I. Introduction

We consider the problem of estimating the current state of a nonlinear discrete-time dynamical system, described by a system of first-order difference equations $$\eqalignno{x(k+1) = &\, f\left (x(k)\right) \cr y(k) = &\, h(x(k))&{\hbox{(I.1)}}}$$ from the past observations , , where . The vector fields , and are continuous with . The variable stands for the state of the system, while the variable represents the measurement output.