Abstract: A method for substantially improving the throughput of circuit simulators is disclosed for arriving at the steady-state of closed-loop self-regulated piecewise-linear or periodically driven piecewise-linear systems. The disclosed method is based on the Newton-Raphson procedure, which enables it to outperform brute-force methods by an order of magnitude in speed, and a special algorithm for the determination of the system sensitivity, which directs it to converge to the solution of systems with high sensitivity with respect to the subinterval timing, where most of the existing methods fail. The method is an iterative procedure with each iteration starting out with the determination of the sensitivity of the final state vector in a switching cycle with respect to the initial state vector of the same switching cycle. This is followed by a Newton-Raphson iteration to predict the initial state vector of a steady-state operation.