Observer design for nonlinear systems using linear approximations

There exist several approaches to the design of observers for nonlinear systems, including the separation of the nonlinear system into a linear part and a nonlinear perturbation of the system with a bounded condition [2], the use of Lie derivatives and the inversion of the Jacobian of a coordinate transformation to obtain the gain of the nonlinear observer [10] and the use of a Lyapunov equation to design the observer for a nonlinear system represented in a special canonical form [8]. The design of observers for linear systems is better understood (see [11], [14]) since in nonlinear theory there is a necessity to use more complex mathematics. Therefore, there exist interest in the development of simpler and general methods to solve the problem of nonlinear state reconstruction. This paper deals with the design of observers for nonlinear systems by using a recent technique in which the nonlinear dynamical system is represented as the limit of a sequence of linear time-varying approximations that converge to the solution of the nonlinear system under a local Lipschitz condition.