Model Reduction Method based on Rational Canonical Form of System Matrix and Krylov Subspace: A Scientific Explanation

For single input and single output time-invariant linear system, a new projection method to obtain reduced models is presented by making use of the rational canonical form of system matrix and the Krylov subspace. At first, the system matrix is transformed to its rational canonical form by use of linear transformation. And then both projection method and Krylov subspace method are used to reduce model. The advantage of this method is the poles of the reduced system are same as those of the original. Thus the reduced system remains the stability when the original system is. This method is more effective than simple Krylov subspace method. Simulation results are show to verify the validity and feasibility of the methods. Numerical examples demonstrate the effectiveness of the method.