${\cal H}_{\infty }$ Filter for Bilinear Systems Using LPV Approach

The aim of this technical note is to present a linear paramater varying (LPV) approach for the design of a functional filter for bilinear systems with a disturbance attenuation specification. The unbiasedness requirement on the observation error is guaranteed by the solution of Sylvester equations obtained by parametrizing the filter gain matrix. This parametrization leads to a non convex optimization problem which is overcome by introducing a constraint on the gain matrix. To take into account the whole set of the inputs in the filter design, an LPV approach is used to obtain the gain matrix guaranteeing the quadratic stability of the observation error and a given level of disturbance attenuation. This approach is then applied to the high gain observer design in order to consider the level of disturbance attenuation.