Finite time convergent observers for nonlinear systems

In this note we consider the state estimation problem for nonlinear systems. In a first step we outline the design of an observer for single output nonlinear systems in observer normal form. The estimate of this observer converges to the exact system state within predefined finite time. This observer is then used in the design of a finite time convergent observer for multiple output systems that are given in block triangular observer normal form. Specifically, the block triangular structure is exploited by recursively designing observers that take the state estimates obtained by the observers for the "previous" blocks into account. As shown the estimation error of the resulting overall observer converges to zero within finite time. The outlined approach is exemplified considering the state estimation of a eights order two link elastic robot.