A Singular Perturbation Method for Order Reduction of Large-Scale Bilinear Dynamical Systems

Abstract In the last years has considerably grown interest in Bilinear Systems, because both for its interest in areas such as biology, enginee ring, chemistry and simplicity. In this paper we solve problem of building a reduced order bilinear model starting from a large scale bill near dynamical system. We do it so that it can replace the high order system, reflecting as good as possible the more important features of its dynamics. The mathematical burden associated with simulation, analysis and control of Large-Scale Bilinear Systems is remarkably simplified because of this reduction. In order to build a lower order bilinear model from an original one we use the Singular Perturbation method. Unfortunately the resultant model is not bilinear in general. For that reason we develope a series of methods wich always lead to a reduced order bilinear model. The method can then be applied repeatedly reducing the dimension on each time. Next we study the relation between the SP method and the linear Aggregation of BLS theory, and we demonstrate that SP method can be viewed as an approximate aggregation technique, giving a procedure to obtain the corresponding aggregation matrices.