Reduced Order State Observer Via Centre Manifold and Sliding-Mode Theories

This study presents a new scheme for the synthesis of reduced order nonlinear state observer. It is based on the centre manifold and the sliding mode theories. The first one is well known as being very useful for the generating of reduced order models at the neighborhood of the Hopf bifurcation point while the sliding-mode theory is widely used for the synthesis of nonlinear state observers. Hence, this study investigates the opportunity to derive reduced order state observers from both theories. This way of proceeding obeys to a different spirit regarding that of the Luenberger observer which is based on the estimating of the only states that are not available from measurements while the proposed scheme gives a method to synthesize a reduced order observer from a reduced order model the output of which is forced to be convergent to the measured system output according to the sliding-modes principle. This permits the obtaining of an estimation of the centre variables based on which the estimation of the full order system state is determined.