Generalized frequency-interval balanced model reduction method

In this paper, a new method for model reduction of bilinear systems is presented. The method is developed in particular for many applications in which one is interested to approximate a system in a given frequency-interval. To this end, new generalized frequency-interval gramians are introduced for bilinear systems. It is shown that these gramians are the solutions to the so-called frequency-interval generalized Lyapunov equations. Algorithms are proposed to solve such equations iteratively. The method is further illustrated with the help of an illustrative example. The numerical results show that the method is more accurate than its previous counterpart which is based on the ordinary gramians.