###### Abstract
Based on linear matrix inequalities and convex optimization techniques, this approach allows to secure better stability, performance and robustness properties and some established benefits over a wide operation region [14; 15; 16]. Thus, applied to DC-DC converters, the first references are found in [17; 18]. In [17], a LMI-based integral fuzzy control for voltage regulation of a basic buck converter with zero-voltage switching (ZVS) is proposed, guaranteeing exponential stability in a broad field of operation. Afterwards in [18] a design methodology of a fuzzy control is presented for a boost converter, ensuring large-signal stability. In particular, through Lyapunov theory, the sufficient-stability conditions in terms of LMIs are adopted considering uncertainty in the parameters. In addition to this, relaxed conditions in the belonging functions are proposed with the purpose of relieving the conservatism of the presented approach. Nonetheless, this work does not describe any experimental prototype and only verifies the effectiveness of the method for a boost converter through simulations. Finally, in [19] an \(H_{\infty}\) fuzzy-control design method is presented for a DC-DC buck converter with input restrictions. Likewise, this work does not show experimental results. Based on the previous statements, the motivation of this work consists in the use of a simple MBFC methodology for the output voltage regulation of two non-minimum phase DC-DC converters, such as boost and buck-boost. In [20; 21] first designs of control synthesis proposed for DC-DC converters through simulations were performed in Matlab. Therefore, through simulations, it is proven that it is possible to ensure the constraintscompliance such as: decay rate and effort control. Besides, starting from the obtained results, it is possible to observe at the same time that a minimum attenuation level is guaranteed between a load current disturbance and regulated output voltage. It is worth noticing, that through the application of the proposed strategy it is possible to consider the saturation of the duty cycle, which allows to attenuate the response of the control signal and maintain within the proper interval. Finally, through a simple and analogue implementation, experimental results of the boost converter are presented, verifying the advantages of the proposed method compared to a non-fuzzy LMI robust control. The rest of the paper is organized as follows. In Section 2, MBFC theory is discussed, which will be used to build the T-S fuzzy models based on buck-boost and boost converters models. Then, in Section 3 the LMIs requirements for design are presented, taking into account the concept of CDP. Then, in Section 4, two examples of fuzzy control based on LMI design are presented for the output voltage regulation problem of buck-boost and boost converters, guaranteeing a certain level of disturbance rejection, a decay rate and control effort limitation. In addition, in this section it is presented a comparison of the proposed controller and a non-fuzzy LMI controller. Experimental results for the boost converter case are also shown in Section 4. Finally, in Section 5 the main conclusions are presented.