Functional H∞ observer design for a class of bilinear systems with time delays

Abstract This work deals with the design of functional observer for a bilinear time-delay system. The system under consideration presents some bounded energy perturbations in its dynamics. In this context, an H ∞ approach is used to provide a guaranteed disturbances attenuation level. Within this chapter, the observation problem is formulated as the stability problem of the estimation error. The unbiasedness of the estimation error system is ensured by the resolution of some linear equalities, which leads to a necessary condition for the existence of the proposed observer and allows the parameterization of the observer gains via a unique gain. Based on a descriptor model transformation, delay-dependent stability conditions are obtained in terms of linear matrix inequalities. A relevant example is provided to show the feasibility and the performances of our result.