Nonlinear observers synthesis based on strongly persistent inputs

In most of the literature, the design of a high gain observer is based on normal forms. In the case where a nonlinear system, which is characterized by a normal form, is observable independently on the input, it is shown here that the gain of this observer does not require any differential equation. In this paper, we also investigate the problem of the high gain observer of a class of nonlinear systems which are not observable independently on the input. It is shown that if the input satisfies some observability condition, then an exponential observer, whose gain derived from a Lyapunov differential equation, can be designed.