Abstract
This paper deals with the problem of observing the state of control systems with a small positive parameter, λ, the small perturbation which can change the order of the system itself. This control system is called the λ-variation system or the singular perturbation system. From the technological point of, view it is the most interesting problem among the problems of systems with parameter variations. The method for designing the adaptive observer that is presented here is considered not only for its order reduction to the λ-variation system, but also for its use for the non-linear system within the linearization.
The design method is applicable
1) to a non-linear system and also to cases in which the parameter λ of the system is small, although the real value is not known precisely.
2) to the (n+m)-th order real physical system by use of the n-th order observer. In this latter application we can reduce the order of the observer and can also simplify the construction of the observer considerably.
