Filippov-Based Stability Analysis Method for Digitally Controlled DC–DC Converters

In contrast to Poincaré map, Filippov’s method is an approach allowing an explicit representation of the Jacobian matrix (the so-called monodromy matrix) which determines the stability of the periodic orbit. However, the existing Filippov’s method was derived for the switching manifold under analog control, which limits its applications to digitally controlled power converters. To fill this gap, Filippov’s method is extended for digitally controlled dc–dc power converters in this article. The analytical expressions of the saltation matrix for digitally controlled power converters with
$k+ 1$
switching states are derived, and the corresponding monodromy matrix is established. Once the steady-state trajectory of the system has been obtained, it is easy to determine both the fast-scale and slow-scale stabilities of the power converter by calculating the eigenvalues of the monodromy matrix. Finally, a digitally controlled dual active bridge (DAB) converter with constant power load (CPL) is taken as an example to verify the correctness of the proposed method.