Model reduction of bilinear systems based on Laguerre series expansion

We present a model reduction method for bilinear systems based on the Laguerre series expansion of the kernels resulting from the Volterra representation theory. By employing a two-sided projection, the reduced order system preserves a desired number of Laguerre coefficients, thereby approximating the original system faithfully. Furthermore, the relationship between the proposed Laguerre-based methods and the moment matching methods is studied, which reveals that these two approaches are equivalent under some specific conditions.