Matrix Exponential

If one chooses to model a power converter in time‐domain, one needs to be familiar with basic numerical methods for evaluating integration and matrix exponentials. This chapter is mainly devoted to matrix exponentials. It describes some of the numerical methods that are important for evaluating matrix exponential. These include inverse Laplace transform, Cauchy–Hamilton method, Pade approximation, scaling and squaring, Krylov subspace methods, and restarted Krylov subspace methods. The chapter shows how we can use the homogeneous state‐space equation to obtain the dynamic model of a dc‐dc converter. It discusses a commonly used integration method, called the Runge–Kutta method. This integration method does not involve iteration, yet is stable and accurate, which is suitable for evaluating differential equations whose system matrix is time‐varying.