Following a unitary procedure, a large-signal stability-oriented design is performed for basic buck, boost and buck-boost converters. Exact nonlinear equations describing the transient state of these converters are written. Positive-definite Lyapunov functions for each converter are defined. Applying the Lyapunov stability theorem, constraints on the parameters of the feedback circuit are derived for ensuring the negativity of each of derivatives of the Lyapunov functions along the converter's differential equations. Computer simulation and laboratory experiments confirmed that the designs that respected the above constraints were stable even for large-signal perturbations.