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Steady state simulation and noise analysis are two essential tools for circuit designers. The algorithms currently available in commonly used simulators are basically limited to the analysis of analog circuits that can be modeled by Lipschitz continuous functions. This is a strong restriction, since current applications are often naturally described by mixed analog-digital models; these models are only piece-wise continuous and Lipschitz condition is not satisfied in the breakpoints. In this paper we propose a method to overcome this limitation by showing how circuits in this class, and, in general, circuits showing discontinuities, can be modeled as hybrid systems. Conventional steady state and noise analysis methods are then extended to this class of circuits. A method to identify the discontinuity points, that, in general, are not known a priori in circuit analysis, is also proposed. With this last addition the method is fully automated and does not require any user intervention.