Modulating function-based fast convergent observer and output feedback control for a class of non-linear systems

In this study, a new observer for a class of non-linear single input/single output systems is proposed. This observer is based on a modulating function with time/output dependent coordinates transformation which transforms the original system into a like-type observer canonical form. In the new coordinates, the initial conditions are annihilated. This property permits to construct a fast convergent deadbeat observer activated after an time delay chosen in order to avoid the singularity of the transformation at the initial time $t=t_{0}$t=t0. The finite-time convergence of the observer is established, i.e. it is shown that the estimation error is bounded in finite time. The proposed observer is used in an output feedback controller design. Using the already established results on the output feedback stabilisation of non-linear input-affine systems, the separation principle is addressed here and the authors show that output feedback controller guarantees under certain conditions the stability of the closed-loop system. Two numerical examples are given to illustrate the effectiveness of the proposed observer-based output feedback controller.