H∞ observer design for a class of nonlinear singular stochastic systems

This paper is about the mean square exponential stability (MSES) H-infinity observer design for a class of nonlinear singular stochastic systems. The system is first transformed such that the observation error can be written in a regular form and the augmented system is admissible. The use of Sylvester-like equations on the error dynamics permit to parameterize all the fillter matrices via a single gain matrix. Then an affine change of coordinate is done on the control inputs to transform the problem into a singular robust stochastic nonlinear problem which is solved using a Lyapunov approach. Finally the mean square exponential stability of the error's system and the H-infinity disturbance attenuation are ensured by the observer designed via the resolution of a LMI which permits to get the gain matrix used to construct the filter matrices.