Design of reduced-order state/unknown input observers based on a descriptor system approach

This paper solves the problem of estimating simultaneously a linear function of the state and unknown input of linear systems with unknown inputs. Here, the problem is conveniently solved by using the descriptor system approach. The observers proposed in this paper are of low-order and do not include derivatives of the outputs. Conditions for the existence of reduced-order observers are derived. Based on the newly derived existence conditions, a step-by-step design procedure is given. A numerical example is given to illustrate the attractiveness and simplicity of the design procedure.