On Observers for Bilinear Systems

This paper deals with a state observer for a bilinear system. The estimation error of the proposed observer converges to zero independently of the input. It is shown that the existence problem of a state observer reduces to a stability problem of a type of bilinear system. Using the results of the present authors on such a stability problem, the design procedure of this observer is presented. Similar results for the minimal order observer are also derived and it is shown that if a full order observer can be designed for a given bilinear system, the minimal order observer can be designed. For the single input system, a simpler design procedure of the minimal order observer is derived. Furthermore for a class of systems which do not satisfy the existence condition of the observer, it is shown that the observer can also be designed for a restricted class of inputs.