LMI Approach for Sliding Mode Control and Analysis of DC-DC Converters

Electrical engineers Aleksandra Lekić and Dušan Stipanović have developed a novel mathematical framework for analyzing sliding mode control in DC-DC power converters. Their paper, published on arXiv with identifier 2604.20240, focuses on the Ćuk converter—a particularly complex topology known for its ability to both step up and step down voltage while providing continuous input and output currents. The researchers employ Linear Matrix Inequalities (LMIs), a powerful tool from control theory, to establish stability conditions for these nonlinear switching systems operating in sliding mode regimes.

The core innovation lies in applying LMI-based stability analysis to systems with nonlinear, sector-bounded perturbations. This approach allows engineers to mathematically determine the maximum allowable nonlinear sector bound, which in turn defines the limit for safely applying linear ripple approximation—a common simplification in power electronics design. The team validated their theoretical framework through simulations of two different switching surfaces of practical interest, demonstrating how converter behavior in steady-state regimes can be rigorously studied and optimized using this mathematical foundation.

Originally published in the journal Tehnika in 2016 and now available on arXiv, this research provides power electronics designers with a more robust analytical toolset. By moving beyond traditional approximation methods, engineers can now better predict stability margins and performance limits in complex switching power supplies, potentially leading to more reliable and efficient power conversion systems across applications from renewable energy to consumer electronics.