Accounting for input constraints in controlling buck power converter

This paper deals with the problem of controlling a DC-to-DC switched power converters of the buck. Due to the fact that the control element is a switch, the control input (duty ratio) is constrained to the interval [0, 1]. The constraint issue has been largely ignored in previous works. In the present paper, this is dealt with by resorting to a saturated version of a regulator, the design of which is carried out on the basis of the average pulse-width-modulation (PWM) model of the controlled circuit. The resulting feedback system turns out to be composed of a linear dynamics block in closed-loop with a nonlinear static element. Applying the circle criterion to such a nonlinear feedback, one gets sufficient conditions, on the design parameters, for the involved feedback to be L₂-stable. If the design parameters satisfy these conditions the regulator meets its objectives