Bifurcation Analysis and Chaos Control in Second‐Order Inverter With Improved Exponential Reaching Law Sliding Mode Control

ABSTRACT In response of the recurrent bifurcation and chaotic phenomena observed in second‐order inverters, this study proposes an improved exponential reaching law sliding mode control strategy, predicated on the principles of sliding mode control and its requisite reaching conditions. A discrete iterative model is formulated utilizing stroboscopic mapping theory, and the intricate dynamic evolution patterns of the inverter are meticulously examined through various analytical tools, including bifurcation diagrams, folding diagrams and spectral diagrams. Furthermore, leveraging the fast‐scale stability theorem, the research investigates the stable operational domain of the system's control parameters. To validate the enhanced performance of the proposed method, numerical simulation experiments were carried out under the traditional exponential reaching law. These simulations encompassed bifurcation analyses of the control parameters and , as well as the circuit parameters , and , along with rapid stability verification. A comparative analysis was also performed against the improved method. The results demonstrate that the system is more prone to chaotic behavior under the traditional exponential reaching law, with a relatively narrow parameter stability region. In contrast, the improved exponential reaching law significantly expands the stable parameter range, enhancing overall system robustness. Furthermore, to mitigate instability caused by parameter perturbations, an extended delayed feedback chaos control strategy was integrated into the improved exponential sliding mode controlled second‐order inverter. Numerical simulations confirmed the feasibility and effectiveness of this chaos control approach. The findings provide valuable insights for the optimized design, dynamic tuning, and reliable steady‐state operation of second‐order inverters.