A convex modeling is accomplished by the construction of a polytope that comprises all possible linearized models of the converter. In order to minimize the polytope volume and, consequently, reduce the conservatism of the proposed solution, the polytope vertices are determined by the polytopic covering of the projections of the uncertainty region. The synthesis of a robust H_∞ state feedback controller is performed by a convex optimization problem based on LMIs. The algorithm includes pole placement restrictions in closed-loop.

One of the states of the system is an unmeasurable tension related to the capacitor, therefore it must be estimated for implementing the state feedback control. Hence, the proposed solution consists in measuring the capacitor current, so that it can be used alongside the output voltage to identify the capacitor ESR and determine the unmeasurable state. Albeit it increases the system complexity, the ESR identification circuit can be used not only for control purposes, but also for monitoring the operational conditions of the converter. The proposed solution is validated by the results of PSIM simulations, considering an specific study of case.