Switched Control for Multi-Mode Affine Systems: Theory and Application to Bidirectional DC-DC Converter

This paper presents a novel switching control strategy with variable timing for multi-subsystem affine switching systems. The main challenge in such systems is to determine when and how transitions should occur to balance stability, efficiency, and performance. To address this, an adaptive algorithm is developed that selects switching instances based on the system state, thereby reducing unnecessary transitions and minimizing switching-induced losses. System stability is established within a Lyapunov-based framework and verified through Bilinear Matrix Inequalities (BMIs), ensuring rigorous theoretical guarantees. Unlike conventional methods that rely on fixed switching patterns or are limited to only a few modes, the proposed approach accommodates an arbitrary number of subsystems, offering greater flexibility and applicability across a wide class of hybrid dynamical systems. The strategy activates switches only when necessary, improving efficiency and reducing operational stress. Its effectiveness is validated through comprehensive simulations and experimental studies, demonstrating enhanced stability, lower transition frequency, and improved dynamic performance.