Bifurcation analysis of a Lyapunov-based controlled boost converter

Robust constrained stabilization of boost DC–DC converters through bifurcation analysis

“…To the best of our knowledge [15] is the only publication that offers a design procedure for controllers used in DC-DC converters that takes into account various bifurcation phenomena and therefore we compare our proposed method with the controller presented in [15].…”

“…More specifically, it has been recently shown [15] that with Lyapunov-based controllers (which use parameter-dependent gains, see (16)) multiple equilibria phenomena are avoided in the absence of a controller mismatch, while they appear far outside the range of feasible variations even in the case of a controller mismatch. Moreover, robust closed-loop stability is guaranteed, provided that input saturation is avoided.…”

“…For instance, let us consider a third gain (15) selected to provide an excellent initial startup response for nominal operating conditions, as in Fig. 4(a).…”

“…In [15], the authors have considered a special form of the state-feedback controller (12) -the so-called Lyapunov-based or stabilizing control-, which is restricted to a single gain γ > 0 design, and takes the form…”

“…For a special form of state-feedback controllers (the so-called Lyapunov-based control) the generation of multiple equilibria using the averaged converter model has been recently studied in [15]. It has been shown that bifurcation phenomena are completely avoided in the absence of controller mismatch, but they appear in the case of a mismatch between the values used by the controller and the real system dynamics.…”