Krylov-Subspace Based Model Reduction of Nonlinear Circuit Models Using Bilinear and Quadratic-Linear Approximations

We discuss Krylov-subspace based model reduction techniques for nonlinear control systems. Since reduction procedures of existent approaches like TPWL and POD methods are input dependent, models that are subject to variable excitations might not be sufficiently approximated. We will overcome this problem by generalizing Krylov-subspace methods known from linear systems to a more general class of bilinear and quadratic-bilinear systems, respectively. As has recently been shown, a lot of nonlinear dynamics can be represented by the latter systems. We will explain advantages and disadvantages of the different approaches and discuss the choice of reasonable interpolation points with regard to optimal approximation results. A nonlinear RC circuit will serve as a numerical test example.