Unknown Input Observer for Bilinear Systems with Gain Optimisation

Abstract

In this paper, full-order state observer design for bounded inputs time-invariant bilinear systems subjected to unknown disturbances is investigated, The proposed approach is based on gain optimisation of both the linear and the bilinear parts of the observation error dynamics. The observer synthesis is subdivided into two main steps, The first step consists on a p-2 norm minimisation of the bilinear part of the observation error dynamics. The second step consists on a choice of the gain matrix of the linear part by checking the minimal solution to an algebraic Riccati equation which ensures an exponential stability of the observation error for all admissible inputs. An important contribution of our work is the use of a mode shift transformation of this linear part such that the detectability of the pair (A, C) becomes an unrequired condition for the stability of the reconstruction error, since only admissible inputs are considered. Sufficient conditions for the existence of this observer are given, These conditions are less conservative than those proposed in the literature. The proposed full-order state observer is applicable to a large class of bilinear systems subjected to unknown disturbances.