Large-signal stability-oriented design of boost regulators based on a Lyapunov criterion with nonlinear integral

Exact nonlinear differential equations of boost pulsewidth modulation converters (either with hard-switching or soft-switching, in continuous and discontinuous conduction mode) are obtained, without using average approximations. An extended system of equations also contains the differential equation of the integrated error between the reference and the output voltage. A positive-definite Lyapunov function is defined, including in its expression a nonlinear integral of type Lurie. Sufficient conditions for the Lyapunov stability of the system are determined. Consequently, constraints on the feedback circuit parameters that assure the large-signal stability of the system are formulated. These constraints relate the parameters of the feedback circuit with the values of the power stage elements, load, switching frequency, steady-state duty-cycle. For different values of the steady-state duty-cycle, graphical boundaries which assure the large-signal stability for all the variation of the load are designed. Simulations and experiments confirm the stability of the design.