We present a direct method for the steady-state and stability\udanalysis of autonomous circuits with transmission lines and generic non-\udlinear elements. With the discretization of the equations that describe the\udcircuit in the time domain, we obtain a nonlinear algebraic formulation\udwhere the unknowns to determine are the samples of the variables directly\udin the steady state, along with the oscillation period, the main unknown in\udautonomous circuits.An efficient scheme to buildtheJacobian matrix with\udexact partial derivatives with respect to the oscillation period and with re-\udspect to the samples of the unknowns is described. Without any modifica-\udtion in the analysis method, the stability of the solution can be computed a\udposteriori constructing an implicit map, where the last sample is viewed as\uda function of the previous samples. The application of this technique to the\udtime-delayed Chua's circuit (TDCC) allows us to investigate the stability of\udthe periodic solutions and to locate the period-doubling bifurcations.
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