The authors propose a method of simulation of static power converters which uses the diagonalization technique of the dynamical matrix to decrease simulation time. This technique leads to a simple analytical solution, allowing a reduction in calculation time. This method allows new independent state variables, and a reduction in the system order. The authors verify that for the structures analyzed, they have observed, on average, a gain in calculation time of the matrix exponential of about 97% using the matrix diagonalization method. The developed algorithm is shown to be a powerful, efficient and, in certain cases, an essential tool for the study of applications in power electronics.