In this paper, the problem of state estimation for a class of uncertain, and possibly unbounded, nonlinear systems is tackled. In order to deal with such a problem, a nonlinear observer is proposed based on a continuous homogeneous and Levant's nth order differentiators. The proposed nonlinear observer provides finite-time convergence and the observer synthesis is formulated in terms of some linear matrix inequalities (LMIs). Moreover, contrary to what the literature shows, the finite-time observer does not require any type of Bounded-Input Bounded-State (BIBS) condition. Some simulation results illustrate the effectiveness of the proposed finite-time observer applied to an unstable nonlinear system.
Bibliographical noteFunding Information:
This work was supported by Consejo Nacional de Ciencia y Tecnología [CVU 270504 project 922].
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- Sliding-mode observer
- finite-time convergence
- nonlinear systems