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This chapter proposes a systematic approach for the synthesis of robust controllers for dc-dc converters. The approach is based on the Linear Matrix Inequalities (LMIs) framework and the associated optimization algorithms. The aim of this approach is to allow the designer to describe the uncertainty of the converter and to deal with the requirements of the application beforehand. The aforementioned dc-dc converters (see Figure 1) are devices that deliver a dc output voltage, with different properties from those in the input voltage (Erickson & Maksimovic, 1999). They are usually employed to adapt energy sources to the load requirements (or vice versa). These devices present several challenges regarding their robust control. First, the converter must maintain a tight regulation or tracking of the output. Moreover, the controller design is focused on maximizing the bandwidth of the closed-loop response in order to reject the usual disturbances that appear in these systems. Finally, the response of the converter must satisfy desirable transient characteristics, as for example, the shortest possible output settling time or the minimum overshoot. Besides of these common requirements, the converter can be affected by uncertainty in its components or by input or output disturbances that may appear.

LMI Robust Control of PWM Converters: An Output-Feedback Approach