State observer design for descriptor bilinear systems

This paper is devoted to the design of causal state observers for singular bilinear systems where the matrix E is singular or rectangular. The proposed method is based on a p-2 norm minimisation of the observation error bilinear part and the use of the minimal solution of some algebraic Riccati equation for the linear part. An important contribution of our work is the use of a pole shift transformation such that the r-detectability of the triple (E, A, C) is a nonrequired condition for the existence of the observer. Sufficient conditions for the existence of the observer are given. Finally, the effectiveness of our approach is illustrated by an application to the simultaneous state and fault vector estimation without a priori knowledge about the dynamics of the fault vector.