Abstract
This paper presents a new method of linearization by augmenting state variables in a Taylor expansion for a nonlinear differential or difference equation which describes nonlinear systems. Regarding every polynomial of the state variable (x) up to the N-th order as a new state variable, an augmented vector (X) is introduced. The vector's dynamic equation which associates with the original nonlinear equation is expanded in a Taylor series truncated at the N-th order with respect to x so that a linear dynamic equation of X is obtained. It has been proved that the approximation error by using the resulting linear equation is on the (N+1)-th order of an infinitesimal.
This paper also proposes a nonlinear observer based on the aforementioned method of linearization for nonlinear systems. The nonlinear observer includes an extended linear observer and a 2nd-order observer as special cases.
The numerical results indicate that both the linearization and the observer given here perform better than the ordinary linearization and observer.
